
    ger                       d Z ddlZddlZddlZddlZddlmZ ddlZddlZddl	Z	ddl
mZmZmZmZmZmZmZmZmZmZ ddlZddlmZ ddlZddlZddlmZmZ ddlmZ ddlmZ dd	l m!Z! dd
l"m#Z#m$Z$m%Z%m&Z& ddl'm(Z( ddl)m*Z* ddl+Zddl,m-Z-m.Z.m/Z/ ddl0m1Z1m2Z2 ddl3m4Z4m5Z5 ddl6m7Z7m8Z8 ddl9m:Z:m;Z; ddl<m=Z= ej>        j?        dk    Z@ej	        dk    o e	jA                    dk    ZBddgZCddZDd ZEd ZF G d d          ZGddZHd ZIejJ        K                    dg d          d              ZL G d! d"          ZM G d# d$          ZN G d% d&          ZO G d' d(          ZP G d) d*          ZQ G d+ d,          ZR G d- d.          ZS G d/ d0          ZT G d1 d2          ZU G d3 d4          ZV G d5 d6          ZW G d7 d8          ZX G d9 d:          ZY G d; d<          ZZ G d= d>          Z[ G d? d@          Z\ G dA dB          Z] G dC dD          Z^ G dE dF          Z_ G dG dH          Z` G dI dJ          Za G dK dL          Zb G dM dN          Zc G dO dP          Zd G dQ dR          Ze G dS dT          Zf G dU dV          Zg G dW dX          Zh G dY dZ          Zi G d[ d\          Zj G d] d^          Zk G d_ d`          Zl G da db          Zm G dc dd          Zn G de df          Zo G dg dh          Zp G di dj          Zq G dk dl          Zr G dm dn          Zs G do dp          Zt G dq dr          Zu G ds dt          Zv G du dv          Zw G dw dx          Zx G dy dz          Zy G d{ d|          Zz G d} d~          Z{dd ej|        ddej}        z  z            z  dd ej|        ddej}        z  z            z  dd ej|        ddej}        z  z            z  dd ej|        ddej}        z  z            z  dd ej|        ddej}        z  z            z  g	fd ej|        ddej}        z  z            dd ej|        ddej}        z  z            z  dd ej|        ddej}        z  z            z  dz  dd ej|        ddej}        z  z            z  dz  dd ej|        ddej}        z  z            z  dz  g	fdd ej|        dej}        z            z  ddd ej|        dej}        z            z  z  ddd ej|        dej}        z            z  z  ddd ej|        dej}        z            z  z  ddd ej|        dej}        z            z  z  ddd ej|        dej}        z            z  z  ddd ej|        dej}        z            z  z  dgfgZ~ G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d¦          Z G dÄ dĦ          Z G dń dƦ          Z G dǄ dȦ          ZdɄ Z G dʄ d˦          Z G d̄ dͦ          Z G d΄ dϦ          Z G dЄ dѦ          Z G d҄ dӦ          Z G dԄ dզ          Z G dք dצ          Z G d؄ d٦          Z G dڄ dۦ          Z G d܄ dݦ          Z G dބ dߦ          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Zd Zd Zd ZejJ                            e@d          d             Zd Zd Zd Zd Zd Zd Zd  Zd Zd Zd ZejJ        K                    dg d          d             Zd Zd Zd	 Zd
 Zd Zd ZejJ        K                    dg d          d             Zd Zd Zd Zd ZÐd ZĐd ZejJ        K                    dd ej        ddg          fd ej        ddg          fd ej        ddg          fd  ej        d!d"g          fg          d#             ZƐd$ Zǐd% ZȐd& Zɐd' ZejJ        K                    d(g d)          d*             ZejJ        K                    d+g d,          d-             ZejJ        K                    d.g d/          d0             Z͐d1 ZejJ        K                    d(g d2          d3             Zϐd4 Z G d5 d6e(j                  Z G d7 d8e(j                  Z G d9 d:e(j                  Z G d; d<e(j                  Z G d= d>          Z G d? d@          ZejJ                            e@dA          dB             ZؐdC ZِdD ZڐdE ZېdF ZܐdG ZݐdH ZސdI ZߐdJ ZdK ZdL ZdM ZdN ZejJ        K                    d(g dO          dP             ZejJ        K                    dQdRdSg          dT             ZejJ        K                    dUddg dVfdWdXg dVfdYdZg d[fg          d\             Zd] Zd^ ZejJ                            ej        d_k    d`          da             Z G db dc          Zdd Z G de df          Z G dg dh          Z G di dj          Z G dk dl          Zdm ZejJ        K                    dne5e2z             do             Zdp Zdq ZejJ        K                    d+drdsg          dt             ZejJ        K                    d.g du          dv             Zdw Zdx Zdy Z G dz d{          Z G d| d}          Z G d~ d          ZdS (  z!
Test functions for stats module
    N)Path)
assert_equalassert_array_equalassert_almost_equalassert_array_almost_equalassert_allcloseassert_assert_warnsassert_array_lesssuppress_warningsIS_PYPY)raises)	typecodesarray)rec_append_fields)special)check_random_state)IntegrationWarningquad	trapezoidcumulative_trapezoid)
argsreduce)xlogy	polygammaentr)distcontinvdistcont   )distdiscreteinvdistdiscrete)FitDataError
_argus_phi)rootfmin)productdarwinx86_64tukeylambdapearson3c                 V    ||  d| }t          t          | |          |           d S )Nz does not have attribute msg)r	   hasattr)abr,   s      Dlib/python3.11/site-packages/scipy/stats/tests/test_distributions.py_assert_hasattrr1   4   s;    
{00Q00GAqMMs######    c                  D    t          t          j        j        d           d S )Nf_gen)r1   scipystatsdistributions r2   r0   test_api_regressionr9   :   s    EK-w77777r2   c                      t          t          j        j        j                  } d t
          D             }d t          D             }g d}||z   |z   }t          t          d |                    }| |k    sJ d S )Nc                     g | ]
}|d          S r   r8   .0dists     r0   
<listcomp>z0test_distributions_submodule.<locals>.<listcomp>A   s    ///d$q'///r2   c                     g | ]
}|d          S r<   r8   r=   s     r0   r@   z0test_distributions_submodule.<locals>.<listcomp>B   s    111DQ111r2   )rv_discreterv_continuousrv_histogramentropytrapzc                 H    t          |                               d           S )N<)str
startswithss    r0   <lambda>z.test_distributions_submodule.<locals>.<lambda>I   s    A(9(9#(>(>$> r2   )setr5   r6   r7   __all__r   r   filter)actual
continuousdiscreteotherexpecteds        r0   test_distributions_submodulerV   ?   s    *233F//h///J11L111H! ! !EH$u,H 6>>IIJJHXr2   c            	       ~   e Zd Zej                            dg d          ej                            dddej        ddg          d                         Zd	 Z	d
 Z
ej                            dg d          d             Zej                            dg d          d             Zd Zej                            dg d          d             Zd Zej        j        ej                            dddg          ej                            dg d          ej                            dddg          ej                            dddg          d                                                             Zej                            dd ej        z  dej        g          ej                            d!g d"          d#                         Zd$ Zej        j        ej                            dd ej        z  d%ej        z  g          d&                         Zej                            d'd(dg          d)             Zd*S )+TestVonMisesk)皙?r   e   xr   r   
   d   c                     d }d } ||dd|            ||dd|            ||dd|            ||dd|            ||dd|            ||dd|           d S )Nc                     t          j        | ||          }t          |                    |          |                    |dt          j        z  |z  z                       d S )Nlocscale   )r6   vonmisesr   pdfnppirY   LrL   r\   vms        r0   check_vonmises_pdf_periodiczHTestVonMises.test_vonmises_periodic.<locals>.check_vonmises_pdf_periodicR   sS    q222Bq		266!q25y1}2E+F+FGGGGGr2   c                     t          j        | ||          }t          |                    |          dz  |                    |dt          j        z  |z  z            dz             d S )Nra   r   rd   )r6   re   r   cdfrg   rh   ri   s        r0   check_vonmises_cdf_periodiczHTestVonMises.test_vonmises_periodic.<locals>.check_vonmises_cdf_periodicV   sl    q222Bq		A "qAIM': ; ;a ?A A A A Ar2   r   r   r]   r8   )selfrY   r\   rl   ro   s        r0   test_vonmises_periodicz#TestVonMises.test_vonmises_periodicO   s    	H 	H 	H	A 	A 	A
 	$#Aq!Q///##Aq!Q///##Aq"a000##Aq!Q///##Aq!Q///##Aq"a00000r2   c                     t          t          j        j        t          j                    t          t          j        j        t          j                   d S N)r   r6   vonmises_liner.   rg   rh   r/   rp   s    r0   test_vonmises_line_supportz'TestVonMises.test_vonmises_line_supportc   s:    U(*RUF333U(*BE22222r2   c                 t    t          j        d          }t          |                    d          d           d S )N   r         ?)r6   re   r   rn   )rp   rk   s     r0   test_vonmises_numericalz$TestVonMises.test_vonmises_numericalg   s1    ^C  BFF1IIs+++++r2   zx, kappa, expected_pdf))rZ   {Gz?g|65?)rZ         9@g?U?)rZ   rx   g"?)       @r{   gDfI?)r}   r|   g1<)r}   rx           c                 j    t           j                            ||          }t          ||d           d S NV瞯<rtol)r6   re   rf   r   )rp   r\   kappaexpected_pdfrf   s        r0   test_vonmises_pdfzTestVonMises.test_vonmises_pdfu   s6     n  E**\666666r2   zkappa, expected_entropy))r   gA	?)   g,eޞ?)r^   gBb9d22)  g
G )  gc                 h    t           j                            |          }t          ||d           d S NvIh%<=r   )r6   re   rE   r   )rp   r   expected_entropyrE   s       r0   test_vonmises_entropyz"TestVonMises.test_vonmises_entropy   s5     .((//!1>>>>>>r2   c                    t          t          d                    }t          j                            |          }t          j                            |          }t          j                            |          }t          j        ddd                              |          }t          j        ddt          j        z  d                              |          }t          j        dddt          j        z  t          |          z  dz                                 |          }t          ||d           t          ||d           d S )	Nvon_mises_rvsr   r   ra   random_staterd   r   atol)
abshashrg   randomdefault_rngr6   re   rvsrh   r   )rp   seedrng1rng2rng3rvs1rvs2rvs3s           r0   test_vonmises_rvs_gh4598z%TestVonMises.test_vonmises_rvs_gh4598   s   4(())y$$T**y$$T**y$$T**~aQa00044$4GG~aQruWA666:::MM~aQ%&ruWSYY%6q%8; ; ;;>3D3;Q;Q 	d////d//////r2   zx, kappa, expected_logpdf))rZ   r{   gEJ?)rZ   r|   goι?)rZ   rx   g0,)r}   r{   gdty)r}   r|   gʹw[A)r}   rx   gc                 j    t           j                            ||          }t          ||d           d S r   )r6   re   logpdfr   )rp   r\   r   expected_logpdfr   s        r0   test_vonmises_logpdfz!TestVonMises.test_vonmises_logpdf   s6     &&q%00e<<<<<<r2   c                 :   t           j                            d          }|                    d          dz  \  }}}t          j        ||                              d           }t          |d           t          j        |j        t           j	                  sJ ||dt           j
        z  z   f} t          j        ||          j        d g|R  }t          |d           t          j        |j        t           j	                  sJ ||dt           j
        z  z   f} t          j        ||          j        d	 g|R d
di}t          t          j        |          |dt           j
        z  z             t          j        |j        t           j                  sJ dS )a   
        Test that the vonmises expectation values are
        computed correctly.  This test checks that the
        numeric integration estimates the correct normalization
        (1) and mean angle (loc).  These expectations are
        independent of the chosen 2pi interval.
           kD +xNn    r]   rb   r   c                     dS Nr   r8   r\   s    r0   rM   z3TestVonMises.test_vonmises_expect.<locals>.<lambda>       A r2   r   rd   c                     dS r   r8   r   s    r0   rM   z3TestVonMises.test_vonmises_expect.<locals>.<lambda>   r   r2   c                 0    t          j        d| z            S )Ny              ?)rg   expr   s    r0   rM   z3TestVonMises.test_vonmises_expect.<locals>.<lambda>   s    BF2a4LL r2   complex_funcN)rg   r   r   r6   re   expectr   
issubdtypedtypefloatingrh   anglecomplexfloating)rp   rngrb   r   lbresboundss          r0   test_vonmises_expectz!TestVonMises.test_vonmises_expect   s    i##$788A+UBnE22299++FFQ}SY44444R!be)^#9enE2229++OOOOQ}SY44444R!be)^#9enE2229:P:P S;AS S SPQS Ssag777}SY(:;;;;;;;r2   rvs_locrd   	rvs_shape)r   r^       חAfix_locTF	fix_shapec                 .   |r|rt          j        d           t          j                            d          }t
          j                            |d||          }ddi}|r||d<   |r||d<   t          t
          j        |t
          j        j	        fi | d S )	NzNothing to fit.r   r   )sizerb   r   fscaler   flocf0)
pytestskiprg   r   r   r6   re   r   _assert_less_or_close_loglikennlf)rp   r   r   r   r   r   datakwdss           r0   test_fit_MLE_comp_optimizerz(TestVonMises.test_fit_MLE_comp_optimizer   s      	+ 	+K)***i##$788~!!)$G/2 " 4 4 !} 	#"DL 	#"DJ%end&+n&9	C 	C=A	C 	C 	C 	C 	Cr2   rb         	kappa_tol))rZ   皙?)      Y@r{   )g     j@r{   c                 z   t           j                            d          }|\  }}t          j        ||                              d|          }t          j                            |          \  }}}	|	dk    sJ t          j        t          j        |          t          j	        |          g          }
t          j        t          j        |          t          j	        |          g          }t          j
        |
                    |                    }t          |d|d           t          |||           d S )	Nr   r   順 r   r   r   r   r   r   )rg   r   r   r6   re   r   fitr   cossinarccosdotr   )rp   r   rb   r   r   tolr   	kappa_fitloc_fit	scale_fitloc_vecloc_fit_vecr   s                r0   test_vonmises_fit_allz"TestVonMises.test_vonmises_fit_all   s    i##$788
s~#U33377EH 8 J J(-(:(:4(@(@%	7IA~~~~(BF3KK566hwABB	'++k2233qs3333ys333333r2   c                 J   t           j                            d          }dt           j        z  }d}t	          j        ||                              d|          }t          j                            ||          \  }}}||k    sJ |dk    sJ t          ||d	
           d S )Nr         ?r]   r   r   r   r   r   r{   r   )	rg   r   r   rh   r6   re   r   r   r   )rp   r   rb   r   r   r   r   r   s           r0   test_vonmises_fit_shapez$TestVonMises.test_vonmises_fit_shape   s    i##$78825j~#U33377S7QQ(-(:(:4c(:(J(J%	7I#~~~~A~~~~yt444444r2   c                 "   g d}t          j        |          }t          j                            ||          \  }}}|t          j        t                    j        k    sJ t          t          j        |t          j        j	        d|           d S )N)g!*Kg4,%OԿgZ۵?g
ge_@g-8gPghn?g<t?g.6@gjb?g0]o@g݅ZgSsgx7W?g%H?g65Jg:m2?g@g;,gM^lsFr   r   )r   r   )
rg   asarrayr6   re   r   finfofloattinyr   r   )rp   rb   r   r   r   r   s         r0   test_vonmises_fit_bad_flocz'TestVonMises.test_vonmises_fit_bad_floc   s    M M M z$(-(:(:4c(:(J(J%	7IBHUOO00000%end&+n&9!#	O 	O 	O 	O 	O 	Or2   signc                    t           j                            d          }t          j        |dz  t           j        z  d                              d|          }|dt           j        z  z   }t          j                            |          \  }}}t          j                            |          \  }}	}
t          ||	           t          ||           |dk    sJ t           j         |cxk     rt           j        k     sn J d S )	Nr   ry   r]   r   r   r      r   )	rg   r   r   r6   re   rh   r   r   r   )rp   r   r   r   shifted_datar   r   r   kappa_fit_shiftedloc_fit_shifted_s              r0    test_vonmises_fit_unwrapped_dataz-TestVonMises.test_vonmises_fit_unwrapped_data  s    i##$788~$s(25.;;;??MP @ R Rag~(-(:(:4(@(@%	7I050B0B<0P0P-?A111	#4555A~~~~v''''"%''''''''r2   N)__name__
__module____qualname__r   markparametrizerg   rh   rq   rv   rz   r   r   r   r   r   xslowr   r   r   r   r   r8   r2   r0   rX   rX   N   s        [S---00[S1aC"8991 1 :9 101$3 3 3, , , [5/ / /0 07 70 07 [6; ; ;< <? ?< <?0 0 0  [8B B BC C= =C C=< < <4 [[YA//[[---88[Yu66[[4-88C C 98 76 98 0/ 
C$ [UTBE\1be$<==[[ +8 +8 +8 9 94 49 9 >=45 5 5 [[UTBE\4"%<$@AA	O 	O BA 	O [Vb!W--
( 
( .-
( 
( 
(r2   rX   c                 X   || j         } | j        |fi |} t          t          |           |           j        |fi |} |||          } |||          }||k    st	          j        ||d          sJ d|v r|d         |d         k    sJ d|v r|d         |d         k    sJ dS dS )a^  
    This utility function checks that the negative log-likelihood function
    (or `func`) of the result computed using dist.fit() is less than or equal
    to the result computed using the generic fit method.  Because of
    normal numerical imprecision, the "equality" check is made using
    `np.allclose` with a relative tolerance of 1e-15.
    Nr   r   r   r   r   )r   r   supertyperg   allclose)r?   r   funcr   mle_analyticalnumerical_optll_mle_analyticalll_numerical_opts           r0   r   r     s     |yTXd++d++N/E$t**d++/====M^T22tM400!111K)+;%HHH 211
 ~~b!T&\11114b!T(^3333 33r2   c           
         ddg}| j         r6t          | j                             d                    }|g dd |         z  }t          t	          |t          j        t          |                                        }g d}t          j        t          d          5   | j
        |fi | d d d            n# 1 swxY w Y   t          j        t          d          5  | 
                    t
          j        g           d d d            n# 1 swxY w Y   t          j        t          d          5  | 
                    t
          j        g           d d d            n# 1 swxY w Y   t          j        t          d	          5  | 
                    |d
           d d d            n# 1 swxY w Y   t          j        t          d          5   | j
        |gdgt          |          dz
  z  R   d d d            d S # 1 swxY w Y   d S )Nr   r   ,)r   f1f2r   rd   r   3All parameters fixed. There is nothing to optimize.matchz#The data contains non-finite valueszUnknown keyword arguments:rd   )extra_keywordzToo many positional arguments.r   )shapeslensplitdictziprg   aranger   r   RuntimeErrorr   
ValueErrornaninf	TypeError)r?   paramnshapes	all_fixedr   s        r0   assert_fit_warningsr  /  sL   XE{ .dk'',,--###HWH--S	#e** 5 56677I99D	|&
' 
' 
' $ $ 	#####$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ 
zB
D 
D 
D  "&               
zB
D 
D 
D  "&               
y(D	E	E	E ( (Q'''( ( ( ( ( ( ( ( ( ( ( ( ( ( (	y(H	I	I	I . .-SZZ!^,----. . . . . . . . . . . . . . . . . .sZ   B88B<?B<!DDD1!EE"%E"F((F,/F,#G>>HHr?   )alpha	betaprimefatiguelifeinvgammainvgauss
invweibull	johnsonsblevylevy_llognormgibratpowerlognormrayleighwaldc                    t          t                    }||          }t          t          |           } t	           | j        | j        g|R  d           t           | j        | j        g|R  t          j
                    t	           | j        | j        g|R  d           t           | j        | j        g|R  t          j
                    dS )zgh-6235r   N)r  r   getattrr6   r   rf   r.   r   r   rg   r  r/   )r?   dctargss      r0   test_supportr/  F  s     x..Ct9D5$D/$///333TV+d+++bfW555/$///333TV+d+++bfW55555r2   c                   &    e Zd Zd Zd Zd Zd ZdS )TestRandIntc                 D    t           j                            d           d S N  rg   r   r   ru   s    r0   setup_methodzTestRandInt.setup_methodY      
	tr2   c                 v   t           j                            ddd          }t          t	          j        |dk               t	          j        |dk              z             t          t          |          dk               t           j                            ddd          }t          t	          j        |          dk               t          |j        j	        t          d         v            t           j                            dd          }t          |dk    |dk     z             t          t          |t          j                  t          t          |                    	           t          j        dd                              d
          }t          |j        j	        t          d         v            d S )Nr      r^   r   rd   2   
AllInteger   .   r+   r   )r6   randintr   r	   numpyallr  shaper   charr   
isinstance
ScalarTypereprr   rp   valsvals      r0   test_rvszTestRandInt.test_rvs\  sZ   }  BS 11	$)$$uy';';;<<<D		S !!!}  BW 55D!!W,---
9\#::;;;mB''sRx()))
3 011tDIIGGGGmB##''**	)L"99:::::r2   c                     t           j        dd         }t          j        |dk    |dk     z  dd          }t          j                            |dd          }t          ||           d S )Nr   $   r   r9  {Gz?)rA  r_wherer6   r@  pmfr   )rp   rY   outrI  s       r0   test_pdfzTestRandInt.test_pdfi  s`    HQrTNk16a"f-z1==}  Ar**!$,,,,,r2   c                    t          j        ddd          }t          j        |          }t          j        |dk    |dk    gd|dz
  dz   d	z  gd          }t
          j                            |dd          }t          ||d
           d S )Nr   rM  r^   r9  r         ?      @r   r|      decimal)	rg   linspacerA  floorselectr6   r@  rn   r   )rp   r\   rY   rR  rI  s        r0   test_cdfzTestRandInt.test_cdfo  s    K2s##KNNlAGQ!V,sQsU1Wv4F.GKK}  Ar**!$R888888r2   N)r   r   r   r6  rK  rS  r]  r8   r2   r0   r1  r1  X  sP          ; ; ;- - -9 9 9 9 9r2   r1  c                   D    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
S )	TestBinomc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestBinom.setup_methodx  r7  r2   c                    t           j                            ddd          }t          t	          j        |dk              t	          j        |dk              z             t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            dd          }t          t          |t                               t          j        dd                              d          }t          t          |t          j                             t          |j        j        t          d         v            d S Nr]         ?r;  r:  r   r=  r   )r6   binomr   r	   rA  rB  rC  r   rD  r   rE  intndarrayrH  s      r0   rK  zTestBinom.test_rvs{  s   {r4g66	$!)$$uy'<'<<===D!!W,---
9\#::;;;koob$''
3$$%%%k"d##''**
3..///	)L"99:::::r2   c                     t           j                            ddd          }t           j                            ddd          }t          |ddd           t          |ddd           d S )Nr^   r   r   rU  r   r   r   r6   rd  rQ  r   )rp   vals1vals2s      r0   test_pmfzTestBinom.test_pmf  sd    S!,,3**sQ7777sQ777777r2   c                    t          j        dd          }t          j        g d          }t	          t          ||                     }|                                }t          ||           t          j        dd          }|                                }t          |d           t          j        dd          }|                                }t          |d           d S )Nrd   ry   )r   ry   r   r~   rU  )	r6   rd  rg   r   sumr   rE   r   r   )rp   r/   
expected_p
expected_hhs        r0   test_entropyzTestBinom.test_entropy  s    K3X///00
%
J77888
IIKK:&&&K3IIKKQK3IIKKQr2   c                 j   t          j                    5  t          j        dt                     t	          t          j        dd                                          d           t	          t          j        dd                                          d           d d d            d S # 1 swxY w Y   d S )Nerrorrd   r   np)	warningscatch_warningssimplefilterRuntimeWarningr   r6   rd  meanstdru   s    r0   test_warns_p0zTestBinom.test_warns_p0  s    $&& 	9 	9!'>:::qA...3355q999qA...2244a888	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9s   BB((B,/B,c                 Z    d}t           j                            d|d          |k    sJ d S )Nr   333333?rU  )qrv  rw  )r6   rd  ppfrp   rv  s     r0   test_ppf_p1zTestBinom.test_ppf_p1  s2    {S11Q666666r2   c                     d}d}t          j        d          }t          j                            |||          }t          j                            |||z            }t          ||d           d S )NglyCgq]\	T3<r   ru  缉ؗҜ<r   )rg   r  r6   rd  rQ  poissonr   )rp   rv  rw  r\   r   refs         r0   test_pmf_poissonzTestBinom.test_pmf_poisson  sh    "IaLLkooa1o**m1q5))Su------r2   c                     d}d}d}t           j                            |||          }t           j                            |||          }t	          ||d           d S )NgJ-DgO
;r   r  r   )r6   rd  rQ  rn   r   )rp   rv  rw  rr   r  s         r0   test_pmf_cdfzTestBinom.test_pmf_cdf  sZ    kooaA&&kooaA&&Su------r2   c                 l    t           j                            ddd          }t          |dd           d S )Nr   r   +?r   r  r   ri  )rp   r   s     r0   test_pmf_gh15101zTestBinom.test_pmf_gh15101  s4    kooau--QU++++++r2   N)r   r   r   r6  rK  rl  rr  r~  r  r  r  r  r8   r2   r0   r_  r_  w  s          	; 	; 	;8 8 8   9 9 97 7 7
. . .. . ., , , , ,r2   r_  c                       e Zd Zd ZdS )TestArcsinec                     t           j                            ddg          }t          |t          j        t          j        g           d S Nr   r   )r6   arcsinerf   r   rg   r  rp   rw  s     r0   test_endpointszTestArcsine.test_endpoints  s<     Mq!f%%Q()))))r2   N)r   r   r   r  r8   r2   r0   r  r    s#        * * * * *r2   r  c                        e Zd Zd Zd Zd ZdS )TestBernoullic                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestBernoulli.setup_method  r7  r2   c                    t           j                            dd          }t          t	          j        |dk              t	          j        |dk              z             t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            d          }t          t          |t                               t          j        d                              d          }t          t          |t          j                             t          |j        j        t          d         v            d S )Nrc  r;  r:  r   r   r=  r   )r6   	bernoullir   r	   rA  rB  rC  r   rD  r   rE  re  rf  rH  s      r0   rK  zTestBernoulli.test_rvs  s
   ""4g"66	$!)$$uy';';;<<<D!!W,---
9\#::;;;o!!$''
3$$%%%od##''**
3..///	)L"99:::::r2   c                    t          j        d          }dt          j        d          z  dt          j        d          z  z
  }|                                }t          ||           t          j        d          }|                                }t          |d           t          j        d          }|                                }t          |d           d S )Nr         пrc  r~   rU  )r6   r  rg   logrE   r   r   )rp   r/   rp  rq  s       r0   rr  zTestBernoulli.test_entropy  s    OD!!26$<<'$rvd||*;;
IIKK:&&&OC  IIKKQOC  IIKKQr2   N)r   r   r   r6  rK  rr  r8   r2   r0   r  r    sA          	; 	; 	;    r2   r  c                       e Zd Zd ZdS )TestBradfordc                     d}t          j        dd          }t          j                            ||          }t          j                            ||          }t          ||           d S )NrZ   )rg   logspacer6   bradfordrn   r  r   )rp   cr\   r  xxs        r0   test_cdf_ppfzTestBradford.test_cdf_ppf  s\    KR  Nq!$$^1%%2r2   N)r   r   r   r  r8   r2   r0   r  r    s#            r2   r  c                   t    e Zd ZdZdZd Zd Zd Zej	        
                    dg d          d             Zd	S )
TestChignT9;g2 >h?@c                 t    t           j                            dd          }t          || j        d           d S )Nr]   r   r   r   )r6   chisfr   CHI_SF_10_4rp   rL   s     r0   test_sfzTestChi.test_sf  s5    ILLQ4+%888888r2   c                 t    t           j                            | j        d          }t	          |dd           d S )Nr   r]   r   r   )r6   r  isfr  r   rp   r\   s     r0   test_isfzTestChi.test_isf   s5    IMM$*A..2E******r2   c                 t    t           j                            d          }t          || j        d           d S )Nr   )df-q=r   )r6   r  r|  r   CHI_MEAN_1000r  s     r0   	test_meanzTestChi.test_mean  s5    INNdN##4-E::::::r2   df, ref))-C6?gQ(݂)r   ńjɮ9?)     @@gWr4'?)    _Bgr$h(?)}Ô%ITgs$h(?c                 r    t          t          j        |                                          |d           d S r   )r   r6   r  rE   rp   r  r  s      r0   rr  zTestChi.test_entropy  s3     		"--//5AAAAAAr2   N)r   r   r   r  r  r  r  r  r   r   r   rr  r8   r2   r0   r  r    s         'K $M9 9 9+ + +; ; ; [Y; ; ;< <B B< <B B Br2   r  c                   &    e Zd Zd Zd Zd Zd ZdS )
TestNBinomc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestNBinom.setup_method  r7  r2   c                    t           j                            ddd          }t          t	          j        |dk                         t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            dd          }t          t          |t                               t          j        dd                              d          }t          t          |t          j                             t          |j        j        t          d         v            d S rb  )r6   nbinomr   r	   rA  rB  rC  r   rD  r   rE  re  rf  rH  s      r0   rK  zTestNBinom.test_rvs   s    |Dw77	$!)$$%%%D!!W,---
9\#::;;;lr4((
3$$%%%l2t$$((++
3..///	)L"99:::::r2   c           	      2   t          t          j        t          j                            ddd                    t          j                            ddd                     t          j        j                            ddd          }t          |d           d S )Ni  i  gp=
ף?r   r   )	r   rg   r   r6   r  logpmfrQ  r5   r   )rp   rJ  s     r0   rl  zTestNBinom.test_pmf+  s    u|223TBBCC((c488	: 	: 	: k ''1a00S!r2   c                     t           j                            g ddd          }t          j        t           j                            g ddd                    }t          ||           d S )N)r   r   r   r   333333@?ru  )r6   r  logcdfrg   r  rn   r   )rp   rI  r  s      r0   test_logcdf_gh16159zTestNBinom.test_logcdf_gh161593  sb    |""<<<3$"??fU\%%lllcT%BBCCc"""""r2   N)r   r   r   r6  rK  rl  r  r8   r2   r0   r  r    sP          	; 	; 	;  # # # # #r2   r  c                       e Zd Zd Zej        j        d             Zej        j        d             Zej        j        d             Z	ej        j        d             Z
d Zd Zd Zd	 Zd
S )TestGenInvGaussc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestGenInvGauss.setup_method;  r7  r2   c                     t          j        dd          }t          j        |                    dd          |j                  \  }}t          |dk    d           d S )Nffffff@      ?  r4  r   r   r   Tr6   geninvgausskstestr   rn   r   rp   gigr   rw  s       r0   test_rvs_with_mode_shiftz(TestGenInvGauss.test_rvs_with_mode_shift>  W     S))|CGGDGAA37KK1QXt$$$$$r2   c                     t          j        dd          }t          j        |                    dd          |j                  \  }}t          |dk    d           d S )N?rc  r  r4  r  r   Tr  r  s       r0   test_rvs_without_mode_shiftz+TestGenInvGauss.test_rvs_without_mode_shiftE  sW     T**|CGGDGAA37KK1QXt$$$$$r2   c                     t          j        dd          }t          j        |                    dd          |j                  \  }}t          |dk    d           d S )NrZ   皙?r  r4  r  r   Tr  r  s       r0   test_rvs_new_methodz#TestGenInvGauss.test_rvs_new_methodL  r  r2   c                     d }t           |dd          d           t           |dd          d           t           |dd          d           d S )Nc                     t          j        | |          }|                    dd          }t          j        ||j                  d         dk    S )Nr  r4  r  r   r   )r6   r  r   r  rn   )rw  r/   r  r   s       r0   my_ks_checkz4TestGenInvGauss.test_rvs_p_zero.<locals>.my_ks_checkU  sG    #Aq))C''t$'77C<SW--a0477r2   r   r  Tr  r  )r   )rp   r  s     r0   test_rvs_p_zerozTestGenInvGauss.test_rvs_p_zeroS  sm    	8 	8 	8
 	[[C(($///[[C(($///[[C(($/////r2   c                     t          t          j        dd                              dd          dt          j        dd                              dd          z             d S )N      rd   r]   r4  r  r   r  )r   r6   r  r   ru   s    r0   test_rvs_negative_pz#TestGenInvGauss.test_rvs_negative_p^  sn    !$**..BT.JJE%c1--11r1MMM	O 	O 	O 	O 	Or2   c                 H   t           j                            dddd          }t          t          j        |ddg          d         dk    d	           d
t          j        ddd          }}t           j                            |dd|z  |          }t          |t          j	        |                              |                     t           j        
                    |dd|z  |          }t          |t          j	        |          
                    |                     d S )Nr  r   r   r4  )r   rw  r/   r   r!  r.  333333?Tr^   r{   r]   )rw  r/   rc   )r6   r  r   r   r  rg   rZ  rf   r   r!  rn   )rp   igmur\   pdf_igcdf_igs         r0   test_invgausszTestGenInvGauss.test_invgaussd  s   """MMU\"js;;;A>EtLLLR[q"--A"&&qDAF"&EEr 2 2 6 6q 9 9:::"&&qDAF"&EEr 2 2 6 6q 9 9:::::r2   c                     t          j        g d          }t          j        ddd          }t          |t          j                            |dd                     d S )N)
g;g8y8?g\}Z?ghܲ<?g&Khdd?g7!L?g	Cf?g_诱?g>0|?gRq?r{   r   r]   ry   r   )rg   r   rZ  r   r6   r  rf   )rp   vals_Rr\   s      r0   
test_pdf_RzTestGenInvGauss.test_pdf_Ro  sd      , , , - - Ka$$ 1 5 5aa @ @AAAAAr2   c                     t          t          j                            ddd          d           t          t          j                            ddd          d           d S )Nr   ry   g    >Ar<  rd   )r   r6   r  rf   ru   s    r0   test_pdf_zerozTestGenInvGauss.test_pdf_zeroz  sT    U&**1c377;;; 	U&**3A66:::::r2   N)r   r   r   r6  r   r   slowr  r  r  r  r  r  r  r  r8   r2   r0   r  r  :  s           [% % % [% % % [% % % [0 0 0O O O	; 	; 	;	B 	B 	B; ; ; ; ;r2   r  c                       e Zd Zd Zd Zd Zej                            dg d          d             Z	ej                            dg d          d             Z
d	 Zd
 Zd Zd Zd Zd ZdS )TestGenHyperbolicc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestGenHyperbolic.setup_method  r7  r2   c                     t          j        g d          }d\  }}}d\  }}|||z  ||z  f}t          j        |||d}t          j        ddd          }	t          |                    |	          |dd	           d S )
N)
gF^T=g{X'=gNunƢsy>g7!t?gɫzI?g̸?g?gq6.?gmPZz?g:PgN?rd   rd   r   ry   r  ra   r]   r   r   r   )rg   r   r6   genhyperbolicrZ  r   rf   
rp   r  lmbdar  betar  deltar.  ghr\   s
             r0   
test_pdf_rzTestGenHyperbolic.test_pdf_r  s           %ud	EuU{DJ/ $Be<<<KR$$q		6>>>>>>r2   c                     t          j        g d          }d\  }}}d\  }}|||z  ||z  f}t          j        |||d}t          j        ddd          }	t          |                    |	          |dd	           d S )
N)
g=R0W<=gEB=g#Nb>g_PG>g! 1Or?gUM?g u./?gfy?gl5\?gkV?r  r  ra   r  r]   r   ư>r   )rg   r   r6   r  rZ  r   rn   r   s
             r0   
test_cdf_rzTestGenHyperbolic.test_cdf_r  s           %ud	EuU{DJ/ $Be<<<KR$$q		6======r2   zx, p, a, b, loc, scale, ref)
)rd   r   r  ry   r  g8ɹvF(;)r	  r]   r  r   r   r   g[Ϡ?)r	  r]   r  g      ?r   r   g ✝`D;)r	        ?r  ):?r   r   gdL;)r   r
  r  r  r   r   gzK^7?)r         r  r  r   r   gj?)r   r  r     r   r   ga=vG:)   r  r   r  r   r   g?)(   r  r   r  r   r   g1bV?)<   r  r   r  r   r   g?c                 t    t           j                            ||||||          }t          ||d           d S Nra   dy=r   )r6   r  rn   r   )	rp   r\   rw  r.   r/   rb   rc   r  rn   s	            r0   test_cdf_mpmathz!TestGenHyperbolic.test_cdf_mpmath  sB     !%%aAqc%GGSu------r2   ))r   r  rW  r   r   r   gC!,?)r   r         @      @r   r   g,Ћf?)r  r   r  r  r   r   rU  )   rd   r   r  ry   r  gm"چ>),  r]   r  r   r   r   g:;)r  r  r   r  r   r   gw=)K   r  r   r  r   r   g3Z0&K<c                 t    t           j                            ||||||          }t          ||d           d S r  )r6   r  r  r   )	rp   r\   rw  r.   r/   rb   rc   r  r  s	            r0   test_sf_mpmathz TestGenHyperbolic.test_sf_mpmath  sB      ##Aq!QCu#EECe,,,,,,r2   c                     g d}d\  }}}d\  ||z  |z  ffdt          dd          D             }t          ||dd	           d S )
N)g@쐧@g@쐧 @g܊B@gvGăi@r  r  c                 Z    g | ]'}t          j        d                     |          (S )ra   )r6   r  moment)r>   ir.  r  r  s     r0   r@   z4TestGenHyperbolic.test_moments_r.<locals>.<listcomp>  sI        2U;;;BB1EE  r2   r   r   r   r   r   )ranger   )	rp   r  r  r  r  vals_usr.  r  r  s	         @@@r0   test_moments_rz TestGenHyperbolic.test_moments_r  s    5 5 5 %ud	EuU{DJ/     1a[[  
 	ae<<<<<<r2   c                     d\  }}}d\  }}|||z  ||z  f}t          j        |||d}t          j        |                    dd          |j                  \  }}	t          |	dk    d           d S )	Nr  r  ra   r  r4  r  r   T)r6   r  r  r   rn   r   )
rp   r  r  r  r  r  r.  r  r   rw  s
             r0   rK  zTestGenHyperbolic.test_rvs  s     %ud	EuU{DJ/ $Be<<<|BFF4F@@"&II1QXt$$$$$r2   c                 2   t          j        ddd          }t          j        |d          t          j        t           j                  j        z  d}}dt          j        |          }}| dz  ||f}t          j        |||d}t          j        |	                    d          |	                    d          d	          d d t           j
        f         }t          |                    |          t          j                            ||          dd
           d S )Nr   r9  r]   rd   r   ra   r{   Gz?r<  r  r   )rg   rZ  float_powerr   float32epssqrtr6   r  r  newaxisr   rf   t)	rp   r  r  r  r  r  r.  r  r\   s	            r0   
test_pdf_tzTestGenHyperbolic.test_pdf_t  s    [B## nR++BHRZ,@,@,DDatrwr{{EAud# $Be<<<KtbffTllB772:FFF1IIuw{{1b))	 	 	 	 	 	r2   c                    dt          j        t           j                  j        d}}}d\  }}|||f}t	          j        |||d}t          j        |                    d          |                    d          d          d d t           j        f         }t          |
                    |          t          j        
                    |          dd	           d S )
Nr   r   )r   r   ra   r{   r%  r<  r  r   )rg   r   r'  r(  r6   r  rZ  r  r*  r   rf   cauchy)	rp   r  r  r  r  r  r.  r  r\   s	            r0   test_pdf_cauchyz!TestGenHyperbolic.test_pdf_cauchy  s    
 "28BJ#7#7#;Qdu	Eud# $Be<<<KtbffTllB772:FFF1IIu|''**	 	 	 	 	 	r2   c                    t          j        ddd          }t          j        t           j                  j        }d\  }}}|||z  ||z  f}t          j        |||d}t          j        ddd          d d t           j        f         }t          |	                    |          t
          j
        	                    ||d          d	d
           d S )Nr  r]   )r   r   r   ra   r  r  r<  r   r   dy=r   )rg   rZ  r   r'  r(  r6   r  r*  r   rf   laplace)	rp   rb   r  r  r  r  r.  r  r\   s	            r0   test_pdf_laplacez"TestGenHyperbolic.test_pdf_laplace   s    k#r2&& $$($uduU{DJ/  $Cu===KR$$QQQ
]3FF1IIu}((1(==	 	 	 	 	 	r2   c           
      p   t          j        ddd          t          j        ddd          t          j        dt          d                    z  t          j        ddd          t          j        ddd          f\  }}}}d	}|||z  ||z  f}t	          j        |||d
}t          j        |                    d          |                    d          d          d d t           j        f         }t          |	                    |          t          j
        	                    |||||          dd           d S )Nr   r  r]   r      r   r^   r   ra   r{   r%  r<  )r.   r/   rb   rc   r   r   )rg   rZ  r&  r   r6   r  r  r*  r   rf   norminvgauss)	rp   r  r  r  r  r  r.  r  r\   s	            r0   test_pdf_norminvgaussz'TestGenHyperbolic.test_pdf_norminvgauss5  s/    Ar2&&Ar2&&r~b%))'D'DDAq"%%D#r**	"tUB uu}dUl3 $Be<<<KtbffTllB772:FFF1IIu)--Ud% . 9 9	 	 	 	 	 	r2   N)r   r   r   r6  r  r  r   r   r   r  r  r"  rK  r,  r/  r3  r8  r8   r2   r0   r  r    s"         ? ? ?,> > >4 [%		< 		< 		< . . . [%	@ 	@ 	@	 	- -	 	-= = =.% % %  $  "  *    r2   r  c                       e Zd Zd Zd Zd Zej                            dg d          d             Z	d Z
d Zd	 Zd
 ZdS )TestNormInvGaussc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestNormInvGauss.setup_methodM  r7  r2   c                     t          j        g d          }t          j        g d          }t          j                            |dd          }t          ||d           d S )N)gp~٧>g @X>g}e?g{)߳?gwH?ir      r>  r   ry   r.   r/   &.>r   )rg   r   r6   r7  rn   r   )rp   r_cdfx_testvals_cdfs       r0   
test_cdf_RzTestNormInvGauss.test_cdf_RP  sr      < < < = =,,,--%))&A)==%d333333r2   c                     t          j        g d          }t          j        g d          }t          j                            |dd          }t          ||d           d S )N)gp϶>g\H55$?geСt&?go NiH?g]u>r=  r   ry   r@  rA  r   )rg   r   r6   r7  rf   r   )rp   r_pdfrC  vals_pdfs       r0   r  zTestNormInvGauss.test_pdf_R\  sp     < < < = =,,,--%))&A)==%d333333r2   zx, a, b, sf, rtol))r   r   r   !7?r   )r  r   r   ?=r  )r   r   r  gy5`?r  )r]   r   r  gMLC9rA  c                     t           j                            |||          }t          |||           t           j                            |||          }t          |||           d S Nr   r6   r7  r  r   r  )rp   r\   r.   r/   r  r   rL   r  s           r0   test_sf_isf_mpmathz#TestNormInvGauss.test_sf_isf_mpmathd  sh     !!!Q**2D))))""2q!,,14((((((r2   c                     ddg}ddg}d}ddg}t           j                            |||          }t          ||dd	           t           j                            |||          }t          ||d
           d S )Nr   r  r   r   rI  rJ  r   r  rh  r  r   rM  )rp   r\   r.   r/   r  rL   r  s          r0   test_sf_isf_mpmath_vectorizedz.TestNormInvGauss.test_sf_isf_mpmath_vectorizedq  s    HF "89!!!Q**2E6666""2q!,,14((((((r2   c                     t          j        dd          }t          j        ddd          }|                    |          }|                    |          }t          ||           d S )Nr   r   r  rd   )r6   r7  rg   r  r  r  r   )rp   dstr\   r  r  s        r0   test_gh8718zTestNormInvGauss.test_gh8718|  s[     A&&IaQVVAYYggbkkQr2   c                 .   d\  }}t          j        |dz  |dz  z
            }||z  |dz  |dz  z  d|z  |t          j        |          z  z  ddd|dz  z  |dz  z  z   z  |z  f}t          |t          j                            ||d                     d S )	Nr   ry   rd   r         @r   r   mvskmoments)rg   r)  r   r6   r7  )rp   r.   r/   gammav_statss        r0   
test_statszTestNormInvGauss.test_stats  s    11q!t$$u9adUAXosQw!bgenn:L/M!a!Q$hAo-.68We066q!V6LLMMMMMr2   c                     d\  }}t          j        g d          }t          j                            |||          }t          |t          j                            |||                     d S )NrU  MbP?ry   r  )rg   r   r6   r7  r  r   rn   )rp   r.   r/   rC  rI  s        r0   test_ppfzTestNormInvGauss.test_ppf  sf    1---..!%%fa33 2 6 6tQ B BCCCCCr2   N)r   r   r   r6  rE  r  r   r   r   rN  rP  rS  r\  r`  r8   r2   r0   r:  r:  L  s          
4 
4 
44 4 4 [0J J JK K
) )K K
)	) 	) 	)     N N ND D D D Dr2   r:  c                   J    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 ZdS )TestGeomc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestGeom.setup_method  r7  r2   c                    t           j                            dd          }t          t	          j        |dk                         t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            d          }t          t          |t                               t          j        d                              d          }t          t          |t          j                             t          |j        j        t          d         v            d S )Nrc  r;  r:  r   r=  r   )r6   geomr   r	   rA  rB  rC  r   rD  r   rE  re  rf  rH  s      r0   rK  zTestGeom.test_rvs  s    z~~d~11	$!)$$%%%D!!W,---
9\#::;;;jnnT""
3$$%%%j""1%%
3..///	)L"99:::::r2   c                 P   t           j                            d          }t          j                            t          j        d          d|          }|j        t           j        k    sJ t          j	        |t          j
        t           j                  j        k              sJ d S )Nl   A: ir   r  )rg   r   r   r6   re  r   r   r   int64rB  iinfoint32max)rp   r   r   s      r0   test_rvs_9313zTestGeom.test_rvs_9313  s     i##O44jnnRVC[[qsnCCyBH$$$$vcBHRX..223333333r2   c                 n    t           j                            g dd          }t          |g d           d S )Nr	  ry   )ry   r   r
  )r6   re  rQ  r   rp   rI  s     r0   rl  zTestGeom.test_pmf  s8    z~~iii--!$(:(:(:;;;;;r2   c                 8   t          j        t          j                            g dd                    }t          j                            g dd          }t          ||dd           t          j                            dd          }t          |d           d S )Nr	  ry   r   r   rh  r   r~   )rg   r  r6   re  rQ  r  r   r   )rp   rj  rk  rJ  s       r0   test_logpmfzTestGeom.test_logpmf  s    uz~~iii5566
!!)))S11u5q9999 j1%%S#r2   c                     t           j                            g dd          }t           j                            g dd          }t	          g d          }t          ||           t          |d|z
             d S )Nr	  ry   ry   rc        ?r   )r6   re  rn   r  r   r   rp   rI  vals_sfrU   s       r0   test_cdf_sfzTestGeom.test_cdf_sf  sr    z~~iii--*--			3//+++,,!$111!'1X:66666r2   c                 :   t           j                            g dd          }t           j                            g dd          }t	          g d          }t          |t          j        |                     t          |t          j        |                      d S )Nr	  ry   rq  )	r6   re  r  logsfr   r   rg   r  log1prs  s       r0   test_logcdf_logsfzTestGeom.test_logcdf_logsf  s    z  C00*""999c22+++,,!$x(8(8999!'28XI+>+>?????r2   c                     t           j                            g dd          }t          g d          }t	          ||           d S )Nrq  ry   )rU  r}   rV  )r6   re  r  r   r   rp   rI  rU   s      r0   r`  zTestGeom.test_ppf  sE    z~~000#66))!$11111r2   c                 f    t          t          j                            dd          dd           d S )N#B;rU  +=r   )r   r6   re  r  ru   s    r0   test_ppf_underflowzTestGeom.test_ppf_underflow  s-    
ue44cFFFFFFr2   c                 v    t          j        d                                          }t          |dd           d S )Ng<,Ԛ?g۩@r   r   )r6   re  rE   r   )rp   rq  s     r0   test_entropy_gh18226zTestGeom.test_entropy_gh18226  s;     Jv&&((,5999999r2   N)r   r   r   r6  rK  rk  rl  ro  ru  ry  r`  r  r  r8   r2   r0   rb  rb    s          	; 	; 	;4 4 4< < <  7 7 7@ @ @2 2 2
G G G: : : : :r2   rb  c                        e Zd Zd Zd Zd ZdS )
TestPlanckc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestPlanck.setup_method  r7  r2   c                     t           j                            g dd          }t          g d          }t	          ||           d S )Nr	  rV  )g|dy?g8'\>ggrU!>)r6   planckr  r   r   r{  s      r0   r  zTestPlanck.test_sf  sQ    |yyy"-- 2 2 2 3 3 	"$11111r2   c                     t           j                            g dd          }t          g d          }t	          ||           d S )N)r       @@     p@r  )g    P.g    h>g    TF)r6   r  rw  r   r   r{  s      r0   
test_logsfzTestPlanck.test_logsf  sJ    |!!"7"7"7??:::;;!$11111r2   N)r   r   r   r6  r  r  r8   r2   r0   r  r    sA          2 2 22 2 2 2 2r2   r  c                   &    e Zd Zd Zd Zd Zd ZdS )TestGennormc                     g d}t           j                            |d          }t           j                            |          }t	          ||           d S Nr	  r   )r6   gennormrf   r2  r   rp   pointspdf1pdf2s       r0   test_laplacezTestGennorm.test_laplace  sM    }  ++}  ((D$'''''r2   c                     g d}t           j                            |d          }t           j                            |d          }t	          ||           d S Nr	  rd   g;f?rc   )r6   r  rf   normr   r  s       r0   	test_normzTestGennorm.test_norm  sO    }  ++z~~fF~33D$'''''r2   c                    t           j                            d           t          j        d          }|                    d          }t          j        ||j                  j        dk    sJ t          j        d          }|                    d          }t          j	                            d          }t          j
        ||          j        dk    sJ t          j        d          }|                    d          }t          j                            dd	          }t          j
        ||          j        dk    sJ d S )
Nr   ry   r   r:  rZ   r   rd   g;f?rc   r   )rg   r   r   r6   r  r   r  rn   pvaluer2  ks_2sampr  )rp   r?   r   rvs_laplacervs_norms        r0   rK  zTestGennorm.test_rvs  s   
	q}S!!hhDh!!|C**1C7777}QhhDh!!m''T'22~c;//6<<<<}QhhDh!!:>>t><<~c8,,3c999999r2   c                    t           j                            d           t          j        ddgddgg          }|                    g d          }t          j        |d d ddf         t          j        d          j                  d         d	k    sJ t          j        |d d ddf         t          j        d          j                  d         d	k    sJ t          j        |d d ddf         t          j        d          j                  d         d	k    sJ t          j        |d d ddf         t          j        d          j                  d         d	k    sJ d S )
Nr   ry   rU  r}   rV  )r   rd   rd   r:  r   rZ   )rg   r   r   r6   r  r   r  rn   )rp   r?   r   s      r0   test_rvs_broadcastingz!TestGennorm.test_rvs_broadcasting  sC   
	q}sBi"b233hhLLLh))|C1aL%-*<*<*@AA!DsJJJJ|C1aL%-*<*<*@AA!DsJJJJ|C1aL%-*<*<*@AA!DsJJJJ|C1aL%-*<*<*@AA!DsJJJJJJr2   N)r   r   r   r  r  rK  r  r8   r2   r0   r  r    sU        ( ( (( ( (: : :"K K K K Kr2   r  c                   Z    e Zd Zej                            dddg          d             ZdS )
TestGibratx, sfx)r  gD.?)  gJ]b<c                     t          t          j                            |          |d           t          t          j                            |          |d           d S )Ng+=r   )r   r6   r'  r  r  rp   r\   sfxs      r0   test_sf_isfzTestGibrat.test_sf_isf  sR     	**Ce<<<<((--qu======r2   N)r   r   r   r   r   r   r  r8   r2   r0   r  r    sV         [X(A(E(G H H> >H H> > >r2   r  c                       e Zd Zd Zej                            dg d          d             Zej                            dg d          d             ZdS )	TestGompertzc                     t           j                            t           j                            dd          d          }t	          |d           d S N0.++r   )r6   gompertzr  rn   r   r  s     r0   test_gompertz_accuracyz#TestGompertz.test_gompertz_accuracy(  sA    Nu~11&!<<a@@6"""""r2   z	x, c, sfx))r   r  g|t?)r   r  g(fMr;)r   r   g[?)g      @r   gg[<c                     t          t          j                            ||          |d           t          t          j                            ||          |d           d S Nr~  r   )r   r6   r  r  r  )rp   r\   r  r  s       r0   r  zTestGompertz.test_sf_isf9  sX    
 	))!Q//5AAAA**322AEBBBBBBr2   c, ref))r  geUT8?)r   gtqq?)r   gs{)r  gN*6c                 d    t          t          j                            |          |d           d S r  )r   r6   r  rE   rp   r  r  s      r0   rr  zTestGompertz.test_entropyH  s/    
 	..q113UCCCCCCr2   N)	r   r   r   r  r   r   r   r  rr  r8   r2   r0   r  r  &  s        # # #" [[ +M +M +M N NC C	N NC [X (E (E (E F FD D	F FD D Dr2   r  c                   Z    e Zd Zej                            dddg          d             ZdS )TestFoldNorm	x, c, ref)r  :0yE>g:0N<?)r  r  g:?c                 f    t          t          j                            ||          |d           d S r   )r   r6   foldnormrn   rp   r\   r  r  s       r0   r]  zTestFoldNorm.test_cdfW  s1     	**1a00#EBBBBBBr2   N)r   r   r   r   r   r   r]  r8   r2   r0   r  r  P  s[         [[+N+M+O P PC CP PC C Cr2   r  c                       e Zd Zej                            dddg          d             Zej                            dg d          d             ZdS )	TestHalfNormr  )r   |N?)r]   Oul2;c                     t          t          j                            |          |d           t          t          j                            |          |d           d S r  )r   r6   halfnormr  r  r  s      r0   r  zTestHalfNorm.test_sf_isfk  sT     	))!,,c>>>>**3//??????r2   x, ref))gWw'&l7g;G<^͛7)C]r2<gE~o-<)r?  g?c                 d    t          t          j                            |          |d           d S r   )r   r6   r  rn   rp   r\   r  s      r0   r]  zTestHalfNorm.test_cdfx  s/     	**1--s??????r2   N)r   r   r   r   r   r   r  r]  r8   r2   r0   r  r  ]  s         [X(?(C(E F F@ @F F@ [X (A (A (A B B@ @B B@ @ @r2   r  c                       e Zd Zej                            dddg          d             Zej                            dg d          d             ZdS )	TestHalfLogisticr  )r^   ]6)   L-c                 d    t          t          j                            |          |d           d S r   )r   r6   halflogisticr  r  s      r0   r  zTestHalfLogistic.test_sf  s0     	*--a00#EBBBBBBr2   q, ref))r  r^   )r  r  )gv?g   .!>)g?g      <c                 d    t          t          j                            |          |d           d S r   )r   r6   r  r  rp   r  r  s      r0   r  zTestHalfLogistic.test_isf  s0    
 	*..q113UCCCCCCr2   Nr   r   r   r   r   r   r  r  r8   r2   r0   r  r    s         [X(D(D(F G GC CG GC [X (K (K (K L LD D	L LD D Dr2   r  c                        e Zd Zd Zd Zd ZdS )TestHalfgennormc                     g d}t           j                            |d          }t           j                            |          }t	          ||           d S r  )r6   halfgennormrf   exponr   r  s       r0   
test_exponzTestHalfgennorm.test_expon  sL     $$VQ//{v&&D$'''''r2   c                     g d}t           j                            |d          }t           j                            |d          }t	          ||           d S r  )r6   r  rf   r  r   r  s       r0   test_halfnormzTestHalfgennorm.test_halfnorm  sS     $$VQ//~!!&!77D$'''''r2   c                     g d}t           j                            |d          }t           j                            |d          }t	          |d|z             d S )Nr	  g
(?rd   )r6   r  rf   r  r   r  s       r0   test_gennormzTestHalfgennorm.test_gennorm  sT     $$VW55}  11D!D&)))))r2   N)r   r   r   r  r  r  r8   r2   r0   r  r    sA        ( ( (( ( (* * * * *r2   r  c                        e Zd Zd Zd Zd ZdS )TestLaplaceasymmetricc                     t          j        g d          }t          j                            |d          }t          j                            |          }t          ||           d S r  )rg   r   r6   laplace_asymmetricrf   r2  r   r  s       r0   r  z"TestLaplaceasymmetric.test_laplace  sX    )))$$'++FA66}  ((d#####r2   c                     t          j        g d          }d}d|z  }t          j                            ||          }t          j                            ||dz  z  |          }t          ||           d S )Nr	  rd   r   )rg   r   r6   r  rf   r   )rp   r  r   kapinvr  r  s         r0   test_asymmetric_laplace_pdfz1TestLaplaceasymmetric.test_asymmetric_laplace_pdf  sr    )))$$5'++FE::'++FE1H,=vFFd#####r2   c           
         t          j        t          j        d           t          j        d          g          }d}t          j                            ||          }t          j                            ||          }t          j                            ||          }t          j        ddg          }t          j        ddg          }t          j        dd	g          }t          j                            ||          }	|}
t          j        	                    ||          }|}t          t          j        ||||	|f          t          j        ||||
|f                     d S )
N   r]   rd   rZ   gMbp?r  gV-?皙?gMb`?)rg   r   r  r6   r  rf   rn   r  r  r  r   concatenate)rp   r  r   r  cdf1sf1r  cdf2sf2ppf1ppf2isf1isf2s                r0   !test_asymmetric_laplace_log_10_16z7TestLaplaceasymmetric.test_asymmetric_laplace_log_10_16  s9   BF2JJ;r

344'++FE::'++FE::&))&%88xu&&xi())hU|$$'++D%88'++C77dCt'DEEdCt'DEE	G 	G 	G 	G 	Gr2   N)r   r   r   r  r  r  r8   r2   r0   r  r    sF        $ $ $$ $ $G G G G Gr2   r  c                      e Zd Zd Zej                            dg d          d             Zej                            dg d          d             Zd Z	d Z
d	 Zd
 Zd Zd Zd Zg dg dg dg ddej        ddddgej         dddddgg dg dg dg	Z ej        e          Zej                            de          d             Zd Zd Zd  Zd! Zd" Zd# Zd$S )%TestTruncnormc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestTruncnorm.setup_method  r7  r2   	a, b, ref))r   r^   r  )333333?ffffff?gܲl)r  g>g+c                 f    t          t          j                            ||          |d           d S N绽|=r   r   r6   	truncnormrE   rp   r.   r/   r  s       r0   rr  zTestTruncnorm.test_entropy  s1    $ 	//155sGGGGGGr2   ))r1  r  ghiɮ9?)r  r  r  )g0.+r  r  )}Ô%Ir  Z_2?c                 f    t          t          j                            ||          |d           d S r  r  r  s       r0   test_extreme_entropyz"TestTruncnorm.test_extreme_entropy  s1      	//155sGGGGGGr2   c           	          t           j                            g ddddgdz  d          }t          j        t          j        dd	dd
dt          j        g          }t          ||           d S )Nr   r   r  ry   H.?r   rd         rU  r      rd   ra   r   fO?l@r   )r6   r  r  rg   r   r  r   r{  s      r0   test_ppf_ticket1131z!TestTruncnorm.test_ppf_ticket1131  n    ""#E#E#EsB()s1uA # 7 78RVQ
Az1bfMNN!$11111r2   c           	          t           j                            g ddddgdz  d          }t          j        t          j        dd	dd
dt          j        g          }t          ||           d S )Nr  r  rU  r   r  rd   ra   r   r  r  r   )r6   r  r  rg   r   r  r   r{  s      r0   test_isf_ticket1131z!TestTruncnorm.test_isf_ticket1131  r  r2   c                    d\  }}t           j                            ||ddd          }t          ||                                cxk     o|                                cxk     o|k     nc            d\  }}t           j                            ||ddd          }t          ||                                cxk     o|                                cxk     o|k     nc            d S )N)ir  r   r   r]   r:  )r]      r6   r  r   r	   minrj  rp   lowhighr\   s       r0   test_gh_2477_small_valuesz'TestTruncnorm.test_gh_2477_small_values  s    	TOT1ab99aeegg........$....///	TOT1ab99aeegg........$..../////r2   c                    d\  }}t           j                            ||ddd          }t          ||                                cxk    o|                                cxk    o|k    nc           t          |||g          f d\  }}t           j                            ||ddd          }t          ||                                cxk     o|                                cxk     o|k     nc            d\  }}t           j                            ||ddd          }t          ||                                cxk     o|                                cxk     o|k     nc            d\  }}t           j                            ||ddd          }t          ||                                cxk     o|                                cxk     o|k     nc            d S )	N)r^   r[   r   r   r]   r:  )r     )'  i'  )i)r6   r  r   r	   r  rj  rI   r  s       r0   test_gh_2477_large_valuesz'TestTruncnorm.test_gh_2477_large_values  s   	TOT1ab99quuww1111!%%''1111T111122CdA4G4GGG 	TOT1ab99aeegg........$..../// 	TOT1ab99aeegg........$....///"	TOT1ab99aeegg........$..../////r2   c                    ddgddgfD ]\  }}t          j        t           j         ||t           j        g          }||z   dz  }t          j                            |||          }t          j                            |||          }t          j                            |||          }t          j        g d          }t          j        g d          }	t          j        g d          }
|d	k     rt          j        g d
          }
t          ||           t          ||	           t          ||
           t          t          j	        |
d         |
d         z            |dz              t          j        g d          }t          j        
                    |||          }t          j        |t          j        |          dz  |g          }t          ||           |d	k     r_t          t          j                            |||          d           t          t          j                            |||          d           n^t          t          j                            |||          d           t          t          j                            |||          d           t          j                            |||          }t          t          j	        ||
d         z            |dz   dz             d S )Nr   r   r  r}   r   r   r   r   rU  rU  r~   r~   )r   d._MT
@BKg?r   r   )r   r  r  r   r   rd   ry   r   ry   rU  gĖy	@gdv*?g,mj%V?r   )rg   r   r  r6   r  rn   r  rf   r   r  r  r   )rp   r  r  xvalsxmidcdfssfspdfsexpected_cdfsexpected_sfsexpected_pdfspvalsppfsexpected_ppfsrf   s                  r0   test_gh_9403_nontail_valuesz)TestTruncnorm.test_gh_9403_nontail_values(  s   a&2r(+  	M  	MICHrvgsD"&9::EHc>D?&&uc488D/$$UC66C?&&uc488DH\\\22M8$8$8$899LH%A%A%ABBMQww ")E)E)E F Fm444\222m444}Q'7a8H'H I I #c	+ + +H]]]++E?&&uc488DHc273<<	+A4%HIIMm444Qww#EO$6$6tS$$G$G$68 8 8#EO$7$7c4$H$H$68 8 8 8 $EO$7$7c4$H$H$68 8 8#EO$6$6tS$$G$G$68 8 8/%%dC66Cs=+;'; < <tDy!mLLLLA 	M  	Mr2   c           	         ddgddgfD ]F\  }}t          j        t           j         ||t           j        g          }||z   dz  }t          j                            |||          }t          j                            |||          }t          j                            |||          }t          j        g d          }t          j        g d          }	t          j        g d          }
|d	k     rt          j        g d
          }
t          ||           t          ||	           t          ||
           t          t          j	        |
d         |
d         z            |dz              t          j        g d          }t          j        
                    |||          }t          j        |t          j        |          dz  |g          }t          ||           t          j                            |||          }t          ||           |d	k     r_t          t          j                            |||          d           t          t          j                            |||          d           n^t          t          j                            |||          d           t          t          j                            |||          d           t          j                            |||          }t          t          j	        ||
d         z            |dz   dz             t          j        ||d          }|d d d          }t          t          j                            |||          t          j                            || |           d d d                    t          t          j                            |||          t          j                            || |           d d d                    t          t          j                            |||          t          j                            || |           d d d                    Hd S )N'   r  ir}   r  r  )r   pGC@Ff<r   r   )r   r/  r.  r   r   rd   ry   r  gEC@g i?gspXio)>r   r  r   )rg   r   r  r6   r  rn   r  rf   r   r  r  r   rZ  )rp   r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  rf   xvals2s                   r0   test_gh_9403_medium_tail_valuesz-TestTruncnorm.test_gh_9403_medium_tail_valuesK  s   r(S#J/ ,	P ,	PICHrvgsD"&9::EHc>D?&&uc488D/$$UC66C?&&uc488DH\\\22M8$8$8$899LH%K%K%KLLMQww " *= *= *= !> !>m444\222m444}Q'7a8H'H I I #c	+ + +H]]]++E?&&uc488DHc273<<+CT%JKKMm444?&&tS$77De,,,Qww#EO$6$6tS$$G$G$68 8 8#EO$7$7c4$H$H$9; ; ; ; $EO$7$7c4$H$H$68 8 8#EO$6$6tS$$G$G$9; ; ;/%%dC66Cs=+;'; < <tDy!mLLLKT2..EDDbDk\F 3 3E3 E E % 2 26D53$ G G" MO O O 2 25#t D D % 3 3FTEC4 H H2 NP P P 3 3E3 E E % 3 3FTEC4 H H2 NP P P PW,	P ,	Pr2   c                     t          t          j        dd                              d          d           t          t          j        dt          j                                      d          d           d S )Ng      *@g      .@      ,@g T?r?  g @gR?)r   r6   r  rn   rg   r  ru   s    r0   test_cdf_tail_15110_14753z'TestTruncnorm.test_cdf_tail_15110_14753z  sr    
 	S1155c::*	, 	, 	,262266s;;*	, 	, 	, 	, 	,r2   )r9  r~   rU  r~   r~   )r  r]   r~   rU  r~   gLFu)r  r   r~   gMFmz%?r~   gſ)r   rd   r~   ghI}?r~   gHNMr   gQ63E?gnl$A?gr1"D?gK8L?gQ63Egr1"D)r   r   gU*? bn?gnA??c3TXʿ)r  r   gU*ҿr6  gnAr7  )r  g"$7"gOxr?gp7`g'>K@casec                     |\  }}}}}}t           j                             ||d          \  }}	}
}t          ||	|
|g||||gd           d S )NrW  rX  FFg<r   )r6   r  r   )rp   r9  r.   r/   m0v0s0k0mvrL   rY   s               r0   test_momentszTestTruncnorm.test_moments  sd    #1b"b"_**1a*@@
1aAq!r2r2&6UCCCCCCr2   c                     t           j                             dt          j        d          \  }}t	          |d           t	          |d           d S )Nr   mvrX  g e3E?g:&A?)r6   r  rg   r  r   )rp   r@  rA  s      r0   test_9902_momentszTestTruncnorm.test_9902_moments  sJ    $$Q$==1Az***Az*****r2   c                     d\  }}t           j                            ||ddd          }t          ||                                cxk     o|                                cxk     o|k     nc            d S )N)r]   r>  r   r   r]   r:  r  r  s       r0   test_gh_1489_trac_962_rvsz'TestTruncnorm.test_gh_1489_trac_962_rvs  sy    	TOT1ab99aeegg........$..../////r2   c                 P   ddt           j         dt           j         t           j         dddddg}dddt           j        ddddd	t           j        t           j        g}t          j                            ||dt          |          f
          }t          j        |          dt          |          fk    sJ t          t          j        ||	                    d          k                         t          t          j        |
                    d          |k                         d S )Nr  r]   r>  ir  r  r   r-  -   r:  r   )axis)rg   r  r6   r  r   r  rC  r	   rB  r  rj  r  s       r0   test_gh_11299_rvszTestTruncnorm.test_gh_11299_rvs  s     BbfWrvgsCS"MB262sBRHOTCHH>>x{{q#c((m++++saeeemm+,,---quu!u}},--.....r2   c                     t          t          j        d          rAt          j                            dddt          j                                                   d S d S )Nr   r  r>  r   r  )r-   rg   r   r6   r  r   r   ru   s    r0   test_rvs_Generatorz TestTruncnorm.test_rvs_Generator  sh    29m,, 	FORa-/Y-B-B-D-D   F F F F F	F 	Fr2   c                    t          j        t           j         t           j         dt           j         dg          }t          j        t           j        t           j        ddt           j        g          }t          j        g d          }g d}t          t	          j        ||                              |          |           t          t	          j        | |                               |           |           d S )Nr]   r?  )r]         @rP  	   r  )gOul"gځ=!gL!g>EG	f g^K[X)rg   r   r  r   r6   r  r  rw  )rp   r.   r/   r\   rU   s        r0   test_logcdf_gh17064z!TestTruncnorm.test_logcdf_gh17064  s    HrvgwRVGR899HbfbfaRV455H***+++ + + 	1--44Q77BBBQB//55qb998DDDDDr2   c                 z    t          j        dd                              d          }d}t          ||           d S )Nr   r   r   gl).0S?)r6   r  r  r   )rp   r   r  s      r0   test_moments_gh18634z"TestTruncnorm.test_moments_gh18634  s@     ob!$$++A..  S!!!!!r2   N)r   r   r   r6  r   r   r   rr  r  r  r
  r  r  r*  r1  r4  rg   r  _truncnorm_stats_datar   rB  rE  rG  rK  rM  rR  rT  r8   r2   r0   r  r    su          [[B B BC CH H	C CH  [[D D DE E
H HE E
H2 2 22 2 20 0 00 0 0&!M !M !MF-P -P -P^, , ,	 	 		1 	1 	1	= 	= 	=	< 	< 	<	
BF						
 &!						
	 	 	
	 	 	
	 	 	;"F %BH%:;;[V%:;;D D <;D
+ + +
0 0 0/ / /F F F	E 	E 	E" " " " "r2   r  c                      e Zd Zej                            dg d          d             Zej                            dg d          d             Zej                            ddd	g          d
             Zej                            dddg          d             Z	ej                            dddg          d             Z
ej                            dddg          d             ZdS )TestGenLogisticx, expected))ig4`n)ig4	ncg)r   gX
=)r^   gh@X)r   gh<c                 n    d}t           j                            ||          }t          ||d           d S )Nr  r   r   )r6   genlogisticr   r   )rp   r\   rU   r  logps        r0   test_logpdfzTestGenLogistic.test_logpdf  s<      ''1--hU333333r2   r  ))r  gTKEl@)r  gJk$@)r   gsF<?)r  7~F<?c                 d    t          t          j                            |          |d           d S N+<r   )r   r6   rZ  rE   r  s      r0   rr  zTestGenLogistic.test_entropy  s0    
 	)11!44cFFFFFFr2   r  )r  r]   g8.)  r  gpT	oc                 f    t          t          j                            ||          |d           d S r  )r   r6   rZ  r  r  s       r0   r  zTestGenLogistic.test_sf  s2     	),,Q22CeDDDDDDr2   	q, c, ref)r{   r  g^ #@)r_  rd   gGFf@c                 f    t          t          j                            ||          |d           d S NgV瞯<r   )r   r6   rZ  r  rp   r  r  r  s       r0   r  zTestGenLogistic.test_isf  2     	)--a33SuEEEEEEr2   )ry   r  gİ@)r%  r  g1a@c                 f    t          t          j                            ||          |d           d S re  )r   r6   rZ  r  rf  s       r0   r`  zTestGenLogistic.test_ppf  rg  r2   )r^   {Gz?g(?)r<  r  g'Tn7c                 f    t          t          j                            ||          |d           d S r   )r   r6   rZ  r  r  s       r0   test_logcdfzTestGenLogistic.test_logcdf  s2     	)00A66%HHHHHHr2   N)r   r   r   r   r   r   r\  rr  r  r  r`  rk  r8   r2   r0   rW  rW    s        [] -I -I -I J J
4 4J J
4 [X (E (E (E F FG G	F FG& [[+L+L+N O OE EO OE [[+I+H+J K KF FK KF [[+I+H+J K KF FK KF [[+N+K+M N NI IN NI I Ir2   rW  c                   D    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
S )TestHypergeomc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestHypergeom.setup_method$  r7  r2   c                    t           j                            dddd          }t          t	          j        |dk              t	          j        |dk              z             t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            ddd          }t          t          |t                               t          j        ddd                              d          }t          t          |t          j                             t          |j        j        t          d         v            d S )Nr  r]   r   r;  r:  r   r=  )r6   	hypergeomr   r	   rA  rB  rC  r   rD  r   rE  re  rf  rH  s      r0   rK  zTestHypergeom.test_rvs'  s   ""2r17";;	$!)$$	$!)$$% 	& 	& 	&D!!W,---
9\#::;;;o!!"a,,
3$$%%%ob!R((,,Q//
3..///	)L"99:::::r2   c                     d}d}d}|}|}t           j                            d|||          }t          |dd           d S )Ni	  r<  ra  rd   gkㅒP?r  )r6   rp  rQ  r   )rp   Mrv  Ntotgoodhgpmfs          r0   test_precisionzTestHypergeom.test_precision3  sO    ##AsD!44E#8"=====r2   c                    t          t          j                            dddd          dd           t          t          j                            dddd          dd           t          t          j                            dddd          dd           t          t          j                            dddd          dd           d S )Nr   rd   r   rU  r  r~   )r   r6   rp  rQ  ru   s    r0   	test_argszTestHypergeom.test_args=  s     	EO//1a;;S"EEEEO//1a;;S"EEEEO//1a;;S"EEEEO//1a;;S"EEEEEr2   c           	          t          dt          j                            dddd          cxk    odk    nc            d S )Nr   r9  io i  if0  rU  )r	   r6   rp  rn   ru   s    r0   test_cdf_above_onez TestHypergeom.test_cdf_above_oneF  sH    U_((XtUCCJJJJsJJJJKKKKKr2   c                 <  	 ddt          j        g d          dz  }d		fd|D             }t          j        g d          }t          ||dd	
           g d}t          j                            |z   d          }g d}t          ||dd	
           d S )Ng    +@g     @)r   ffffff@333333@r   gffffff@@r        @     @c                 Z    g | ]'}t           j                            z   |          (S r8   )r6   rp  r  )r>   eatenorangespearsquantiles     r0   r@   z1TestHypergeom.test_precision2.<locals>.<listcomp>Q  sC     * * * !!(GeOWeLL * * *r2   )r   gpR(g㘍R2gJޱ p9g?Mf=
G?r   r   gƠ>r   )g     @r  g     @g     @g     @)r   r  g)9g"1)rg   r   r   r6   rp  r  )
rp   fruits_eatenr   rU   	quantilesres2	expected2r  r  r  s
          @@@r0   test_precision2zTestHypergeom.test_precision2J  s     x = = =>>D* * * * * *(* * *8 9 9 9 : :XAD9999 0//	!!)Wu_guMM>>>	iad;;;;;;r2   c                 `   t          j        ddd          }|                                }t          j        ddg          }t          j        t          ||                     }t          ||           t          j        ddd          }|                                }t          |d           d S )Nr   r   rc  r   r~   )	r6   rp  rE   rg   r   rn  r   r   r   )rp   hgrq  ro  rp  s        r0   rr  zTestHypergeom.test_entropy]  s    _Q1%%JJLLXtTl++
fU:z::;;;
:&&&_Q1%%JJLLQr2   c                     d}d}d}d}t           j                            ||||          }d}t          ||d           d}d	}d
}d}t           j                            ||||          }d}t          ||d           d S )Nr      cA    .A     j@gor   rX  r   @  X  r  g_7	j$r>  )r6   rp  rw  r   rp   rY   rr  rv  rs  resultrU   s          r0   r  zTestHypergeom.test_logsfi  s     &&q!Q22FHa8888&&q!Q22 FHb999999r2   c                 D   d}d}d}d}t           j                            ||||          }d}t          ||d           d}d	}d
}d}t           j                            ||||          }d}t          ||d           d}d	}d}d}t           j                            ||||          }d}t          ||d           t	          j        g d          }d	}d
}d}t           j                            ||||          }t	          j        dd          }t          ||d           d S )Nr   r  r  r  g)\Ur   rX  r  r  r<  r  g*@Vr>  }      ra  gר)r  r  r  )r6   rp  r  r   rg   r   fullr  s          r0   rk  zTestHypergeom.test_logcdf  sM    ''1a33FHa8888 ''1a33&FHb9999''1a33 FHb9999
 H\\\""''1a3371122FHb999999r2   N)r   r   r   r6  rK  rw  ry  r{  r  rr  r  rk  r8   r2   r0   rm  rm  #  s          
; 
; 
;> > >F F FL L L< < <&
 
 
: : :0,: ,: ,: ,: ,:r2   rm  c                       e Zd Zej                            dg d          d             Zej                            dg d          d             Zd Zd Z	ej                            d	d
dg          d             Z
dS )TestLoggammaz	x, c, cdf))r   rd   g;Y%?)r      gRٲa6_<)gHr_  gi|e?)r_  g6l?)i+rZ   g֬CCf9)irc  g ֺlc                     t           j                            ||          }t          ||d           t           j                            ||          }t          ||d           d S r   )r6   loggammarn   r   r  )rp   r\   r  rn   rw  ys         r0   r  zTestLoggamma.test_cdf_ppf  sb     Nq!$$3U++++NsA&&15))))))r2   zx, c, sf))r   r  gQOu3;)   r^   g\Z{0)r  r_  geɐ?)ig{Gzd?gr0T?c                     t           j                            ||          }t          ||d           t           j                            ||          }t          ||d           d S r   )r6   r  r  r   r  )rp   r\   r  r  rL   r  s         r0   r  zTestLoggamma.test_sf_isf  sb     Na##2E****Nr1%%15))))))r2   c                 j    t           j                            dd          }t          |dd           d S )Nrd   g     @r~  r   )r6   r  r   r   )rp   lps     r0   r\  zTestLoggamma.test_logpdf  s6    
 ^""4++G%000000r2   c                     t          j        g d                              dd          }|D ]?\  }}}}}t          j                            |d          }t          |||||gd           @d S )N)ry   g"~jg46<@g oŏ      @rU  g	h"lxgQ?gZd;333333@g      (@g{/L@g??gгYҿgh|?5?r   r   msvkrX  r   rX  )rg   r   reshaper6   r  r   )rp   tabler  r|  varskewkurtcomputeds           r0   r\  zTestLoggamma.test_stats  s          
 wr1~~ 	 ). 	1 	1$AtS$~++Av+>>H%hsD$0G./1 1 1 1 1	1 	1r2   r  rZ   r_  c                    t           j                            |d          }t          j        |                                          sJ t           j                            |          }t          j        t          j        ||k               t          |                    }|
                    d          }|j        dcxk     r|j        k     sn J d S )Nr   r:  r  )confidence_levelry   )r6   r  r   rg   isfiniterB  median	binomtestcount_nonzeror  proportion_cir  r  )rp   r  r\   medbtestcis         r0   rK  zTestLoggamma.test_rvs  s     Nqv.. {1~~!!##### n##A&& 0S 9 93q66BB  % 88v%%%%bg%%%%%%%%r2   N)r   r   r   r   r   r   r  r  r\  r\  rK  r8   r2   r0   r  r    s         [[E E EF F* *F F* [ZB B BC C
* *C C
*1 1 11 1 1 [S3,//& & 0/& & &r2   r  c                   ^    e Zd Zg dZej                            de          d             ZdS )TestJohnsonsu))r  r   r   g?r  )r   r   r   gH';vIh%,=)r   r   r   g?x7r  r9  c                     |\  }}}}}t          t          j                            |||          |d           t          t          j                            |||          ||           d S Nr  r   )r   r6   	johnsonsur  r  rp   r9  r\   r.   r/   r  r   s          r0   r  zTestJohnsonsu.test_sf_isf	  j    1aS**1a33ReDDDD++B155qsCCCCCCr2   Nr   r   r   casesr   r   r   r  r8   r2   r0   r  r    sX        ; ; ;E [VU++D D ,+D D Dr2   r  c                   ^    e Zd Zg dZej                            de          d             ZdS )TestJohnsonb))r  r   r   g?Hz>)r  r   r   g0jA:r  )g!?r   r   gQbF5r  r9  c                     |\  }}}}}t          t          j                            |||          |d           t          t          j                            |||          ||           d S )Nr  r   r   )r   r6   r#  r  r  r  s          r0   r  zTestJohnsonb.test_sf_isf  r  r2   Nr  r8   r2   r0   r  r    sX        = = =E [VU++D D ,+D D Dr2   r  c                       e Zd Zd Zd Zd Zd Zd Zej	        
                    dddg          d	             Zd
 Zej	        
                    dddg          d             Zd ZdS )TestLogisticc                     t          j        dd          }t          j                            |          }t          j                            |          }t          ||           d S Nr  r  )rg   rZ  r6   logisticrn   r  r   rp   r\   r  r  s       r0   r  zTestLogistic.test_cdf_ppf(  sS    KR  Nq!!^""2r2   c                     t          j        dd          }t          j                            |          }t          j                            |          }t          ||           d S r  )rg   rZ  r6   r  r  r  r   r  s       r0   r  zTestLogistic.test_sf_isf.  sS    KR  Na  ^""2r2   c                     d}d}t          t          j                            d|z
            |           t          t          j                            |          |           d S )Ng      <gg|EA@r   )r   r6   r  r  r  )rp   rw  desireds      r0   test_extreme_valuesz TestLogistic.test_extreme_values4  sV    !#**1q5117;;;**1--w77777r2   c                 t    t           j                            g d          }g d}t          ||d           d S )N)r	  r   r]   )gm\  .g9B.gO& $r   r   )r6   r  r   r   )rp   r[  rU   s      r0   test_logpdf_basiczTestLogistic.test_logpdf_basic;  sI    ~$$\\\22) ) ) 	hU333333r2   c                 l    t           j                            ddg          }t          |ddg           d S )Nrx   r  )r6   r  r   r   rp   r[  s     r0   test_logpdf_extreme_valuesz'TestLogistic.test_logpdf_extreme_valuesC  s7    ~$$c4[11 	TD$<(((((r2   zloc_rvs,scale_rvs)g9x&?gi '?)gB"?gs^&?c                    t           j                            d||          }d }t          |t           j                            |          |f          j        }t           j                            |          }t          ||d           d S )Nr^   r   rb   rc   c                    | \  }}t          |          }t          j        t          j        ||z
  |z            dt          j        ||z
  |z            z   z            |dz  z
  }t          j        ||z
  |z  t          j        ||z
  |z            dz
  t          j        ||z
  |z            dz   z  z            |z
  }||fS Nr   rd   )r  rg   rn  r   )inputr   r.   r/   rv  x1x2s          r0   r   z#TestLogistic.test_fit.<locals>.funcO  s    DAqD		AqA~..RVTAXN3335 6 689A>B$(a&$(a0014&$(a001467 8 8:;<B r6Mr2   r  gKH9r   )r6   r  r   r#   	_fitstartr\   r   r   )rp   loc_rvs	scale_rvsr   r   expected_solution
fit_methods          r0   test_fitzTestLogistic.test_fitI  s     ~!!sy!II	 	 	 !u~'?'?'E'EM    	^''--
 	
$5EBBBBBBr2   c                     t           j                            ddd          }t          t           j        |           t          t           j        |d           t          t           j        |d           d S )Nr^   ry   rd   r  r   r   r   )r6   r  r   r   rp   r   s     r0   test_fit_comp_optimizerz$TestLogistic.test_fit_comp_optimizera  sd    ~!!s1!==%end;;;%endCCCC%end1EEEEEEr2   
testlogcdfTFc                     t          j        g d          }|r t          j                            |          }n t          j                            |           }g d}t          ||d           d S )N)r  r     r<  ra  )     g      g%h9fg?~T}%mgCx^&ْV瞯<r   )rg   r   r6   r  r  rw  r   )rp   r  r\   r  rU   s        r0   test_logcdfsf_tailsz TestLogistic.test_logcdfsf_tailsg  s     H00011 	)%%a((AA$$aR((AF F F8%000000r2   c                     t          j        g ddgdz  z   dgdz  z             }t          t          j        |           d S )N)	i5%   +   rI  rI  0   6   7   :   ;   r   =   rQ  )rg   r   r   r6   r  r  s     r0   test_fit_gh_18176zTestLogistic.test_fit_gh_18176u  sT     x>>>$(#&(TAX. / / 	&end;;;;;r2   N)r   r   r   r  r  r  r  r  r   r   r   r  r  r  r  r8   r2   r0   r  r  &  s            8 8 84 4 4) ) ) [03J3K3M N NC CN NC,F F F [\D%=991 1 :91< < < < <r2   r  c                   &    e Zd Zd Zd Zd Zd ZdS )
TestLogserc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestLogser.setup_method  r7  r2   c                    t           j                            dd          }t          t	          j        |dk                         t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            d          }t          t          |t                               t          j        d                              d          }t          t          |t          j                             t          |j        j        t          d         v            d S )Nrc  r;  r:  r   r=  r   )r6   logserr   r	   rA  rB  rC  r   rD  r   rE  re  rf  rH  s      r0   rK  zTestLogser.test_rvs  s    |733	$!)$$%%%D!!W,---
9\#::;;;lt$$
3$$%%%l4  $$Q''
3..///	)L"99:::::r2   c                 f    t           j                            dd          }t          |d           d S )Nr   r}  g&Y3)r6   r  rQ  r   rp   r@  s     r0   test_pmf_small_pzTestLogser.test_pmf_small_p  s1    LQ&& 	7#####r2   c                 d    t           j                            d          }t          |d           d S )Nr  gW  ?)r6   r  r|  r   r  s     r0   test_mean_small_pzTestLogser.test_mean_small_p  s/    Ld## 	;'''''r2   N)r   r   r   r6  rK  r   r  r8   r2   r0   r  r  ~  sP          	; 	; 	;$ $ $( ( ( ( (r2   r  c            	          e Zd Z ej        d          d             Zej                            dej	        ej
        g          ej                            dg d          ej                            dg d          ej                            d	d
dgdd
gf          d                                                 Zej                            dej	        dfej
        dfg          d             ZdS )TestGumbel_r_lfunctionscopec                 @    t           j                            d          S r3  rg   r   r   ru   s    r0   r   zTestGumbel_r_l.rng      y$$T***r2   r?   r  r   r   r   r  rZ   r   r   zfix_loc, fix_scaleTFc                     |                     d|||          }t                      }|r|dz  |d<   |r|dz  |d<   t          ||fi | d S )Nr^   )r   rb   rc   r   rd   r   r   )r   r  r   )	rp   r?   r  r  r   	fix_scaler   r   r   s	            r0   r  z&TestGumbel_r_l.test_fit_comp_optimizer  s|     xxSgY%(  * * vv  	'"Q;DL 	+&]DN 	&dD99D99999r2   z	dist, sgnr   r   c                     |t          j        g d          z  }|                    |          \  }}t          ||dz             t          |dd           d S )N)r   r   r   r   r   r   r   gW  @g   @g3qtw>r  r   )rg   r   r   r   )rp   r?   sgnzrb   rc   s         r0   r  zTestGumbel_r_l.test_fit  sf     :::;;;XXa[[
U 	S!334445DAAAAAAr2   N)r   r   r   r   fixturer   r   r   r6   gumbel_rgumbel_lr  r  r8   r2   r0   r  r    s=       V^*%%%+ + &%+ [Venen%EFF[Y


33[[***55[1#UmeT];= =: := = 65 43 GF
:  [[ENA+>,1NB+?+A B BB BB BB B Br2   r  c                      e Zd Zd Zd Z ej        d          d             Zej        	                    d          ej        
                    ddd	g          ej        
                    d
dd	g          ej        
                    dddg          d                                                 Zej        
                    ddd	g          ej        
                    d
dd	g          ej        
                    dddg          ej        
                    dd  eddgd          D                        ej        d          d                                                             Z ej        d          d             Zd Zd ZdS )
TestParetoc                 	   t          j                    5  t          j        dt                     t          j                            dd          \  }}}}t          |t          j                   t          |t          j                   t          |t          j	                   t          |t          j	                   t          j                            dd          \  }}}}t          |t          j                   t          |t          j                   t          |t          j	                   t          |t          j	                   t          j                            dd          \  }}}}t          |d           t          |t          j                   t          |t          j	                   t          |t          j	                   t          j                            dd          \  }}}}t          |d           t          |t          j                   t          |t          j	                   t          |t          j	                   t          j                            d	d          \  }}}}t          |d
           t          |d           t          |t          j	                   t          |t          j	                   t          j                            dd          \  }}}}t          |d           t          |d           t          |t          j	                   t          |t          j	                   t          j                            dd          \  }}}}t          |d           t          |d           t          |dt          j        d          z             t          |t          j	                   t          j                            dd          \  }}}}t          |d           t          |d           t          |dt          j        d          z             t          |t          j	                   t          j                            dd          \  }}}}t          |d           t          |d           t          |dt          j        d          z             t          |d           d d d            d S # 1 swxY w Y   d S )Nrt  ry   rW  rX  rU  r  rV  r}   r  g?grq@rc        @gffffff?gK~?g      2@g۶m۶m?r  UUUUUU?gqq?      $@      @g%I$I?gQ?gUUUUUU@grq?g88Nb@)rx  ry  rz  r{  r6   paretor   rg   r  r  r   r)  rp   r@  rA  rL   rY   s        r0   r\  zTestPareto.test_stats  sk    $&& 7	N 7	N!'>:::++C+@@JAq!QBF###BF###BF###BF###++C+@@JAq!QBF###BF###BF###BF###++C+@@JAq!QC   BF###BF###BF###++C+@@JAq!QC   BF###BF###BF###++C+@@JAq!QAy)))A2333BF###BF###++C+@@JAq!QAs###At$$$BF###BF###++C+@@JAq!QAy)))A2333A	277+;+;;<<<BF###++C+@@JAq!QAy)))Az***A027;3G3GGHHHBF###++C+@@JAq!QAy)))A2333A	RWW-=-==>>>ALMMMo7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	Ns   R8SS Sc                     d}d}d}t           j                            ||d|          }||z  |z  }t          ||           d S )Ng    eArd   r  r   ra   )r6   r  r  r   )rp   r\   r/   rc   rw  rU   s         r0   r  zTestPareto.test_sf  sO    LOOAqauO55!Ga<8$$$$$r2   r  r  c                 @    t           j                            d          S r3  r	  ru   s    r0   r   zTestPareto.rng  r
  r2   z2ignore:invalid value encountered in double_scalarsr   r   rd   r   r   	rvs_scaler   c                 ,   t           j                            d||||          }t           j                            |dd          d         }t           j                            |dd          d         }t           j                            |dd          d         }||cxk    r|cxk    rdk    sn J t           j                            d|||dz   |          }t           j                            |d	          \  }	}
}t	          |dz   |                                           |dz
  }|j        d         }t	          |	|t          j        t          j	        ||                                z                      z             t	          |
d           d S )
Nr^   r   r/   rc   rb   r   r   p=
ף?)r   r   )r   fix_b)r   fbrd   r   )
r6   r  r   r   r   r  rC  rg   rn  r  )rp   r   r   r   r   r   shape_mle_analytical1shape_mle_analytical2shape_mle_analytical3shape_mle_a	loc_mle_ascale_mle_a
data_shiftndatas                 r0   r  zTestPareto.test_fit  s    |SIY$+#   ? ? !& 0 0A$ 0 G G J % 0 0AT 0 J J1 M % 0 0A$ 0 G G J%)> . . . .%. . . .)-. . . . . . |SIY%,q[   E E.3l.>.>t!.>.L.L+Y[1_dhhjj111AX
 #[RVBF:jnn6F6F+F$G$GHHH	J 	J 	JY"""""r2   rZ   fix_shape, fix_loc, fix_scalec                     g | ]}d |v |	S Fr8   r>   rw  s     r0   r@   zTestPareto.<listcomp>4  (     - - -A!&!  !+r2   TFr   repeatignoreinvalidc                     t           j                            d||||          }i }	|r||	d<   |r||	d<   |r||	d<   t          t           j        |fi |	 d S )Nr^   r"  r   r   r   )r6   r  r   r   
rp   r   r   r   r   r   r  r   r   r   s
             r0   r   z&TestPareto.test_fit_MLE_comp_optimizer0  s     |SIY$+#   ? ?  	#"DJ 	#"DL 	'&DN%elDAADAAAAAr2   c           	          d\  }}}t           j                            |||dt          j                            d                    }t          t           j        |           d S )N)r   r   r   r^   ið& r  )r6   r  r   rg   r   r   r   )rp   rC  locationrc   r   s        r0   test_fit_known_bad_seedz"TestPareto.test_fit_known_bad_seedF  sa    
 ")x|xS-/Y-B-B7-K-K   M M%elD99999r2   c                     t          t          j                   t          t          t          j        j        g dd           t          t          t          j        j        g ddd           d S )Nr	  rd   r   )r   rd   r   r   r   r   r   )r  r6   r  assert_raisesr!   r   ru   s    r0   test_fit_warningszTestPareto.test_fit_warningsP  sg    EL)))lEL$4iiiaHHHHlEL$4iiia	  	  	  	  	  	 r2   c                     t           j                            ddd|          }t          |d           t           j                            |          }d S )Ni~r   r^   )rb   r/   r   r   r   )r6   r  r   r   r   )rp   r   r   r   s       r0   test_negative_datazTestPareto.test_negative_dataX  sK    |DACcJJ$"""
 LT""r2   N)r   r   r   r\  r  r   r  r   r   filterwarningsr   r  r%   rg   errstater   r<  r@  rB  r8   r2   r0   r  r    s%       :N :N :Nx% % % V^*%%%+ + &%+ [ !1 2 2[[1a&11[YA//[[1a&11# # 21 0/ 212 2
#. [[2q'22[YA//[[1a&11[<- -$q)I)I)I - - -. . R["""B B #". . 21 0/ 32B R[""": : #":     # # # # #r2   r  c                      e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zej                            d
dg dfdddd ej        d          z  ej        gfdddd ej        d          z  dgfdg dfg          d             Zd ZdS )TestGenparetoc                 r   dD ]i}t          j        |          }t          j                            |          \  }}t          |d           t          t          j        |                     jt          j        d          }t          j                            |          \  }}t          ||gddg           d S )NrU  r~   r~          ry   )	rg   r   r6   	genpareto_get_supportr   r	   isposinfr   )rp   r  r.   r/   s       r0   test_abzTestGenpareto.test_abc  s     	$ 	$A
1A?//22DAqBBKNN#### JsOO++A..1AS	*****r2   c                    t          j        d          }t          j        ddd          }t	          |                    |          t           j                            |                     t	          |                    |          t           j                            |                     t	          |                    |          t           j                            |                     t          j        ddd          }t	          |	                    |          t           j        	                    |                     d S )Nr~   r  r   r  r9  rU  r]   )
r6   rJ  rg   rZ  r   rf   r  rn   r  r  rp   rvr\   r  s       r0   test_c0zTestGenpareto.test_c0p  s     _r"""K3##q		5;??1#5#5666q		5;??1#5#5666a%+.."3"3444KB##q		5;??1#5#566666r2   c                    t          j        d          }t          j        ddd          }t	          |                    |          t           j                            |                     t	          |                    |          t           j                            |                     t	          |                    |          t           j                            |                     t          j        ddd          }t	          |	                    |          t           j        	                    |                     t	          |
                    d	          d           d S )
Nr  rO  r   r  r9  r~   rU  r]   r   )r6   rJ  rg   rZ  r   rf   uniformrn   r  r  r   rP  s       r0   test_cm1zTestGenpareto.test_cm1|  s   _s###K3##q		5=#4#4Q#7#7888q		5=#4#4Q#7#7888a%-"2"21"5"5666KB##q		5=#4#4Q#7#7888 			!a(((((r2   c                    t          j        d          }t          |                    t          j                  |                    t          j                  gddg           t          t	          j        |	                    t          j                                       t          j        d          }t          |                    t          j                  |                    t          j                  gddg           t          t	          j        |	                    t          j                                       t          j        d          }t          |                    t          j                  |                    t          j                  gddg           t          t	          j        |	                    t          j                                       d S )NrZ   rO  r~   rU  r  )
r6   rJ  r   rf   rg   r  rn   r	   isneginfr   rp   rQ  s     r0   
test_x_infzTestGenpareto.test_x_inf  sC   _s###82r(CCCBIIbf--..///_r"""82r(CCCBIIbf--..///_s###82r(CCCBIIbf--../////r2   c                    t          j        ddd          }dD ]}t          j                            ||          }dD ]7}t          j                            |||z             }t          ||d           8t          j                            ||          }dD ]7}t          j                            |||z             }t          ||d           8d S )	Nr   r]   r9  r   r   r~  g+r  r   )r~  r~  )rg   rZ  r6   rJ  rf   r   rn   )rp   r\   r  pdf0dcpdfccdf0cdfcs           r0   test_c_continuityzTestGenpareto.test_c_continuity  s    K2r"" 		8 		8A?&&q!,,D% 8 8**1a"f55d77777?&&q!,,D$ 8 8**1a"f55d777778		8 		8r2   c           	      t   t           j        t          j        ddd          t          j        dddd          d	t          j        ddd          z
  f         }d
D ]\}t          j                            ||          }dD ]7}t          j                            |||z             }t          ||d           8]d S Nr  r{   rZ   baser   r9  FendpointrU  )r~   r  r\  r   )rg   rO  r  rZ  r6   rJ  r  r   )rp   r  r  ppf0r^  ppfcs         r0   test_c_continuity_ppfz#TestGenpareto.test_c_continuity_ppf      E"+eT444+dArE:::r{5$S9999: ;  	8 	8A?&&q!,,D% 8 8**1a"f55d777778	8 	8r2   c           	      t   t           j        t          j        ddd          t          j        dddd          d	t          j        ddd          z
  f         }d
D ]\}t          j                            ||          }dD ]7}t          j                            |||z             }t          ||d           8]d S rd  )rg   rO  r  rZ  r6   rJ  r  r   )rp   r  r  isf0r^  isfcs         r0   test_c_continuity_isfz#TestGenpareto.test_c_continuity_isf  rl  r2   c           	      \   t           j        t          j        ddd          t          j        dddd          d	t          j        ddd          z
  f         }d
D ]P}t	          t
          j                            t
          j                            ||          |          |d           Qd S )Nr  r{   rZ   re  r   r9  Frg  rU  )r  gC]r2r   gV瞯Ҽr   r   )	rg   rO  r  rZ  r   r6   rJ  rn   r  )rp   r  r  s      r0   test_cdf_ppf_roundtripz$TestGenpareto.test_cdf_ppf_roundtrip  s    E"+eT444+dArE:::r{5$S9999: ; / 	+ 	+AEO//0C0CAq0I0I1MME+ + + + +	+ 	+r2   c                 j    t           j                            dddd          }t          |d           d S )Nr  r{   r   r   gpEȜ)r6   rJ  rw  r   r  s     r0   r  zTestGenpareto.test_logsf  s4    $$T3155122222r2   zc, expected_statsr   )r   r   rd   r  r   r  gqq@r]   rd   gqq?g      ?g$I$	?rq?r  gll0@r   )ry   UUUUUU?r   333333c                 n    t           j                             |d          }t          ||dd           d S )NrW  rX  r   r   rh  )r6   rJ  r   )rp   r  expected_statsr  s       r0   r\  zTestGenpareto.test_stats  s;     &&q&&99UGGGGGGr2   c                 h    t           j                            d          }t          |dd           d S )Nr  gvǼ
  ?r   r   )r6   rJ  r  r   )rp   rA  s     r0   test_varzTestGenpareto.test_var  s3    O%%,5999999r2   N)r   r   r   rM  rR  rU  rY  rb  rk  rp  rr  r  r   r   r   rg   r)  r  r\  rz  r8   r2   r0   rF  rF  b  sA       + + +
7 
7 
7) ) )0 0 08 8 88 8 88 8 8+ + +3 3 3 [
\\\	
T2gbgajj="&1	2
]T7271::$5v>	?
"""	#	%& &H H& &H: : : : :r2   rF  c                   8    e Zd Zd Zd Zd Zd Zd Zd Zd Z	dS )	TestPearson3c                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestPearson3.setup_method  r7  r2   c                    t           j                            dd          }t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            d          }t          t          |t                               t          j        d                              d          }t          t          |t          j                             t          |j        j        t          d         v            t          t          |          dk               d S )NrZ   r;  r:  AllFloatry   r   )r6   r)   r   r	   rA  rC  r   rD  r   rE  r   rf  r  rH  s      r0   rK  zTestPearson3.test_rvs  s    ~!!#G!44D!!W,---
9Z#88999n  %%
3&&'''nS!!%%a((
3..///	)J"77888CAr2   c                    t           j                            dg d          }t          |t	          j        g d          d           t           j                            dd          }t          |t	          j        dg          d           t           j                            g d	d          }t          |t	          j        g d
          d           d S )Nrd   r~   rZ   r  )gtT?g+q?g?r  r   r  rZ   ND}i?r  r   r   r   r   )r  gj?gdC?gs?g'M?)r6   r)   rf   r   rg   r   rm  s     r0   rS  zTestPearson3.test_pdf  s    ~!!!___55bh'K'K'KLL!	# 	# 	# 	#~!!"c**bh
|444@@@@~!!"4"4"4c::bh (@ (@ (@ A AGK	M 	M 	M 	M 	M 	Mr2   c                 h   t           j                            dg d          }t          |t	          j        g d          d           t           j                            dd          }t          |dgd           t           j                            g d	d          }t          |g d
d           d S )Nrd   r  )grE?gTp]0?g~?r  r   r  rZ   g E&"J?r  )giZ*J?gh+8w?gcK?g|<x6?gG?)r6   r)   rn   r   rg   r   rm  s     r0   r]  zTestPearson3.test_cdf  s    ~!!!___55bh'K'K'KLL!	# 	# 	# 	#~!!"c**zl6666~!!"4"4"4c:: ? ? ?EI	K 	K 	K 	K 	K 	Kr2   c                     g d}ddt           j                            |          }fd|D             }t          ||           d S )Nr  r   r   ry   ry   r5  c                 l    g | ]0}t          t          j        |          j                  d          1S r<   )r   r6   r)   rf   )r>   r  neg_infx_evals     r0   r@   z<TestPearson3.test_negative_cdf_bug_11186.<locals>.<listcomp>	  sG     ' ' ' --17FCCAF ' ' 'r2   )r6   r)   rn   r   )rp   skewsr!  int_pdfsr  r  s       @@r0   test_negative_cdf_bug_11186z(TestPearson3.test_negative_cdf_bug_11186  su     !  ~!!&%00' ' ' ' ' %' ' 'h'''''r2   c                 6   t           j                            dd          }t          |d           t	          |t
          j                  sJ t           j                            dd          }t          |d           t	          |t
          j                  sJ d S )Nr   rd   r   r  )r6   r)   r  r   rE  rg   number)rp   r  s     r0   test_return_array_bug_11746z(TestPearson3.test_return_array_bug_11746	  s     &&q!,,VQ&"),,,,,&&q(33VQ&"),,,,,,,r2   c                    g d}d}t           j                            t           j                            ||          |          }t	          ||           t          j        dgdgg          }t          j        dd          }t	          t           j                            ||          t           j                            | |                      t	          t           j                            ||          t           j        	                    | |                      t	          t           j                            ||          t           j        
                    ||                       d S )Nr  ry   r   r  r   rd   )r6   r)   r  rn   r   rg   r   rZ  rf   r  r  )rp   r  r  r   r  r\   s         r0   test_ppf_bug_17050zTestPearson3.test_ppf_bug_17050	  s?    !  n  !3!3FE!B!BEJJV$$$ x$#((KA**1d33**A2u55	7 	7 	7**1d33))1"te44	6 	6 	6**1d33++Au555	7 	7 	7 	7 	7r2   N)
r   r   r   r6  rK  rS  r]  r  r  r  r8   r2   r0   r|  r|    s          	 	 	M M MK K K	( 	( 	(	- 	- 	-7 7 7 7 7r2   r|  c                   8    e Zd Zd Zd Zd Zd Zd Zd Zd Z	dS )	
TestKappa4c                     g d}d}dD ]T}t           j                            |||          }t           j                            ||           }t	          ||           Ud S )N)r~   rZ   r  ry   rU  )
gffffffr  r   皙ɿ皙rZ   r  ry   rU  ffffff?)r6   kappa4rn   rJ  r   rp   r\   rq  rY   rI  	vals_comps         r0   test_cdf_genparetozTestKappa4.test_cdf_genpareto'	  sr        	- 	-A<##Aq!,,D++Ar22ID),,,,	- 	-r2   c                    t          j        ddd          }d}t          j        ddd          }t          j                            |||          }t          j                            ||          }t          ||           d S )Nr>  r   r]   r~   r  r   )rg   rZ  r6   r  rn   
genextremer   r  s         r0   test_cdf_genextremezTestKappa4.test_cdf_genextreme2	  st    KAr""KAr""|1a(($((A..	i(((((r2   c                     t          j        ddd          }d}d}t          j                            |||          }t          j                            |          }t          ||           d S )Nr   r]   rU  r~   )rg   rZ  r6   r  rn   r  r   r  s         r0   test_cdf_exponzTestKappa4.test_cdf_expon;	  sa    K2r""|1a((KOOA&&	i(((((r2   c                     t          j        ddd          }d}d}t          j                            |||          }t          j                            |          }t          ||           d S )Nr>  r   r]   r~   )rg   rZ  r6   r  rn   r  r   r  s         r0   test_cdf_gumbel_rzTestKappa4.test_cdf_gumbel_rD	  sc    KAr""|1a((N&&q))	i(((((r2   c                     t          j        ddd          }d}d}t          j                            |||          }t          j                            |          }t          ||           d S )Nr>  r   r]   r  r~   )rg   rZ  r6   r  rn   r  r   r  s         r0   test_cdf_logisticzTestKappa4.test_cdf_logisticM	  sc    KAr""|1a((N&&q))	i(((((r2   c                     t          j        ddd          }d}d}t          j                            |||          }t          j                            |          }t          ||           d S )Nr>  r   r]   rU  )rg   rZ  r6   r  rn   rT  r   r  s         r0   test_cdf_uniformzTestKappa4.test_cdf_uniformV	  sc    KAr""|1a((M%%a((	i(((((r2   c                 0    t          j        dd           d S r  )r6   r  ru   s    r0   test_integers_ctorzTestKappa4.test_integers_ctor_	  s     	Qr2   N)
r   r   r   r  r  r  r  r  r  r  r8   r2   r0   r  r  &	  s}        	- 	- 	-) ) )) ) )) ) )) ) )) ) )    r2   r  c                   ,    e Zd Zd Zd Zd Zd Zd ZdS )TestPoissonc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestPoisson.setup_methodf	  r7  r2   c                     t          j        d          }t          j                            g d|          }d|dz  |dz  dz  g}t          ||           d S )Nrd   r   r   rd   ry   r   )rg   r  r6   r  rQ  r   )rp   ln2rI  rU   s       r0   test_pmf_basiczTestPoisson.test_pmf_basici	  sX    fQii}  C00QQq)h'''''r2   c                     t           j                            g dd          }g d}t          ||           t           j                            dd          }t          |d           d S )Nr  r   )r   r   r   ffffff?r   r   )r6   r  rQ  r   intervalr   )rp   rI  rU   r  s       r0   test_mu0zTestPoisson.test_mu0p	  sc    }  A..994***=))$22Xv&&&&&r2   c                    t           j                            dd          }t          t	          j        |dk                         t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            d          }t          t          |t                               t          j        d                              d          }t          t          |t          j                             t          |j        j        t          d         v            d S )Nry   r;  r:  r   r=  r   )r6   r  r   r	   rA  rB  rC  r   rD  r   rE  re  rf  rH  s      r0   rK  zTestPoisson.test_rvsy	  s    }  7 33	$!)$$%%%D!!W,---
9\#::;;;m$$
3$$%%%mC  $$Q''
3..///	)L"99:::::r2   c           	         d}t           j                             |d          }t          |||t          j        d|z            d|z  g           t          j        g d          }t           j                             |d          }||t          j        ddt          j        d          z  gt          j        ddgf}t          ||           d S )	Ng      0@rW  rX  rU  )r~   rU  r}   r   rd   ry   )r6   r  r   rg   r)  r   r  )rp   r  r  rU   s       r0   r\  zTestPoisson.test_stats	  s    $$R$88RR#b& ABBBXooo&&$$R$88RVQ"'!**537GH)))))r2   N)r   r   r   r6  r  r  rK  r\  r8   r2   r0   r  r  e	  s_          ( ( (' ' '	; 	; 	;* * * * *r2   r  c                   V    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd ZdS )	TestKSTwoc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestKSTwo.setup_method	  r7  r2   c                    dD ]}t          j        dd|z  d|z  ddd|z  z
  dg          }d|z  |z  }t          j                            |dz             }|dk    rt          j        |          nd}t          j        dd||z  ddt          j                            d|          z  z
  t          dd|z  z
  d          dg          }t          j
                            ||          }t          ||           d S )Nr   rd   r   r]   r^   r   r   ry   r   rU  rd   r~   )rg   r   r5   r   gammalnr   r6   ksoner  rj  kstworn   r   )rp   rv  r\   v1lgelgrU   rD  s           r0   r]  zTestKSTwo.test_cdf	  s   ) 	0 	0A !SUAaCaAgq9::Aa%!B&&qs++B!#q26":::aCxArCx!"Qu{~~c1'='=%=!=!$Q2Xs!3!3!$!& ' 'H {q!,,HHh////#	0 	0r2   c                    t          j        ddd          }dD ]}t          j        dd|z  d|z  ddd|z  z
  dg          }d|z  |z  }t          j                            |dz             }|dk    rt          j        |          nd}t          j        ddd||z  z
  dt          j        	                    d|          z  t          d|z  d          dg          }t          j        	                    ||          }t          ||           d S )Nr   r   r  r  ry   rU  rd   )rg   rZ  r   r5   r   r  r   r6   r  r  r  r  r   )rp   r\   rv  r  r  r  rU   rt  s           r0   r  zTestKSTwo.test_sf	  s   K1b!!) 	/ 	/A!SUAaCaAgq9::Aa%!B&&qs++B!#q26":::aCxc!"R#X!"5;>>#q#9#9!9!$QrT3!4 5 5H knnQ**GGX....	/ 	/r2   c                 
   t          j        ddd          dd          }g d}|D ]]}|t          j        |          z  }t          j                            ||          }t          j        |          }t          |d           ^d S )Nr   rd   r  r   )r<  r^   r  i  r   r   r  )rg   rZ  r)  r6   r  rn   diffr   )rp   r\   ns_xxnprobsdiffss          r0   test_cdf_sqrtnzTestKSTwo.test_cdf_sqrtn	  s    
 K1b!!!""%,,, 	+ 	+Bbgbkk!BKOOB++EGENNEeT****		+ 	+r2   c                     t          j        ddd          }dD ]U}t          j                            ||          }t          j                            ||          }t          |d|z
             Vd S Nr   r   r  r  )rg   rZ  r6   r  rn   r  r   )rp   r\   rv  rD  rt  s        r0   ru  zTestKSTwo.test_cdf_sf	  so    K1b!!) 	= 	=A{q!,,HknnQ**G%hG<<<<	= 	=r2   c                    t          j        ddd          }dD ]l}|t          j        |          z  }t          j                            ||          }t          j                            ||          }t          |d|z
             md S r  )rg   rZ  r)  r6   r  rn   r  r   )rp   r\   rv  r  rD  rt  s         r0   test_cdf_sf_sqrtnzTestKSTwo.test_cdf_sf_sqrtn	  s    K1b!!) 	= 	=ARWQZZB{r1--HknnR++G%hG<<<<		= 	=r2   c                 0   t          j        ddd          }dD ]|}||d|z  k             }t          j                            ||          }d|k     |dk     z  }t          j                            ||          }t          ||         ||         d           }d S )	Nr   r   r  r  ry   r%  r  r   )rg   rZ  r6   r  rn   r  r   rp   r\   rv  r  rD  condrI  s          r0   test_ppf_of_cdfzTestKSTwo.test_ppf_of_cdf	  s    K1b!!) 	= 	=A1s1u9B{r1--HLX_5D;??8Q//DDJ4t<<<<<	= 	=r2   c                 0   t          j        ddd          }dD ]|}||d|z  k             }t          j                            ||          }d|k     |dk     z  }t          j                            ||          }t          ||         ||         d           }d S )	Nr   r   r  r  ry   rU  r  r   )rg   rZ  r6   r  r  r  r   )rp   r\   rv  r  vals_isfr  rI  s          r0   test_isf_of_sfzTestKSTwo.test_isf_of_sf	  s    K1b!!) 	= 	=A1s1u9B{r1--HLX^4D;>>(A..DDJ4t<<<<<	= 	=r2   c                 V   t          j        ddd          }dD ]}|t          j        |          z  |d|z  k             }t          j                            ||          }d|k     |dk     z  }t          j                            ||          }t          ||         ||                    d S )Nr   r   r  r  ry   rU  )rg   rZ  r)  r6   r  rn   r  r   r  s          r0   test_ppf_of_cdf_sqrtnzTestKSTwo.test_ppf_of_cdf_sqrtn	  s    K1b!!) 	2 	2Abgajj.!c!e),B{r1--HLX^4D;??8Q//DDJ41111	2 	2r2   c                 V   t          j        ddd          }dD ]}|t          j        |          z  |d|z  k             }t          j                            ||          }d|k     |dk     z  }t          j                            ||          }t          ||         ||                    d S )Nr   r   r  r  ry   r  )rg   rZ  r)  r6   r  r  r  r   )rp   r\   rv  r  rt  r  rI  s          r0   test_isf_of_sf_sqrtnzTestKSTwo.test_isf_of_sf_sqrtn	  s    K1b!!) 	2 	2Abgajj.!c!e),BknnR++GKGdN3D;??7A..DDJ41111	2 	2r2   c                     t          j        ddd          dd          }dD ]R}t          j                            ||          }t          j                            ||          }t          ||           Sd S r  )rg   rZ  r6   r  r  rn   r   )rp   r  rv  r  rD  s        r0   r`  zTestKSTwo.test_ppf	  st    Aq"%%abb)) 	- 	-A**B{r1--HHe,,,,	- 	-r2   c           	         g d}t          j        g d          }t          j        g dg dg dg dg dg dg          }t          |          D ]y\  }}|t          j        d	          z  t          j        t           j        d	z  |z            z  }t          j                            ||          }t          |||         d
           zd S )N)r]   r<  r^   r  ra  r   )r   gUUUUUU?ry   r   rd   r   )gRT>gr	?gK5
?gn
"5?gU
?gk?)g&6#>gb
E>gI5?g\?g;?g%1?)g6>gL>g<?g䓀^?gO|6$?g qO?)g}+: >gwQ9>gH{?g]qv(?g)~/v?gmJ?)gV27J=gGk(>gWX?gY?g{0`?gZ
H?)g_R=g4>g̪?gT_@?g<e?g2?rd   h㈵>r   )
rg   r   	enumerater  r)  rh   r6   r  rn   r   )rp   r  ratiosrU   idxrv  r\   rD  s           r0   test_simard_lecuyer_table1z$TestKSTwo.test_simard_lecuyer_table1	  s    +**888998- - -- - -- - -- - -- - -- - -
    mm 	@ 	@FC"RWRU1WQY%7%77A{q!,,HHhsm$?????	@ 	@r2   N)r   r   r   r6  r]  r  r  ru  r  r  r  r  r  r`  r  r8   r2   r0   r  r  	  s          0 0 0(/ / /+ + += = == = == = == = =2 2 22 2 2- - -@ @ @ @ @r2   r  c                        e Zd Zd Zd Zd ZdS )TestZipfc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestZipf.setup_method"
  r7  r2   c                    t           j                            dd          }t          t	          j        |dk                         t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            d          }t          t          |t                               t          j        d                              d          }t          t          |t          j                             t          |j        j        t          d         v            d S )Nr  r;  r:  r   r=  r   )r6   zipfr   r	   rA  rB  rC  r   rD  r   rE  re  rf  rH  s      r0   rK  zTestZipf.test_rvs%
  s    z~~c~00	$!)$$%%%D!!W,---
9\#::;;;jnnS!!
3$$%%%joo!!!$$
3..///	)L"99:::::r2   c                 v   t           j                             d          \  }}t          t          j        |                     t          |t          j                   t           j                             dd          \  }}t          t          j        ||g                                                      d S )Nffffff@r.   r  skr.   rY  )r6   r  r	   rg   r  r   r  rB  r  s        r0   rB  zTestZipf.test_moments0
  s    z#&&1AQz#t441BKA''++---.....r2   N)r   r   r   r6  rK  rB  r8   r2   r0   r  r  !
  sA          	; 	; 	;/ / / / /r2   r  c                   &    e Zd Zd Zd Zd Zd ZdS )TestDLaplacec                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestDLaplace.setup_method;
  r7  r2   c                    t           j                            dd          }t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            d          }t          t          |t                               t          j        d                              d          }t          t          |t          j                             t          |j        j        t          d         v            t          t           j                            d          d u           d S )Nr  r;  r:  r=  r   r  )r6   dlaplacer   r	   rA  rC  r   rD  r   rE  re  rf  rH  s      r0   rK  zTestDLaplace.test_rvs>
  s    ~!!#G!44D!!W,---
9\#::;;;n  %%
3$$%%%nS!!%%a((
3..///	)L"99:::""3''t344444r2   c                    d}t          j        |          }|                     d          \  }}}}d}t          j        | |dz             }|                    |          }	t          j        |	|dz  z            t          j        |	|dz  z            }}
t          ||fd           t          ||f|
||
dz  z  dz
  fd	d
           d S )NrU  rW  r  r   rd   r   r  rV  r~  r  r   )r6   r  rg   r  rQ  rn  r   r   )rp   r.   dlr@  rA  rL   rY   rs  r  ppm2m4s               r0   r\  zTestDLaplace.test_statsI
  s    ^AXXf%%
1aYr1Q3VVBZZ2q5!!26"RU(#3#3BaVV$$$ARAX] 3%dKKKKKKr2   c                     t          j        d          }t          j        |          }|                    d          \  }}}}t	          ||fd           t          ||fd           d S )Nr}   rW  )r~   r~   )r        
@)rg   r  r6   r  r   r   )rp   r.   r  r@  rA  rL   rY   s          r0   test_stats2zTestDLaplace.test_stats2V
  se    F2JJ^AXXf%%
1aaVX&&&A
+++++r2   N)r   r   r   r6  rK  r\  r  r8   r2   r0   r  r  :
  sS          	5 	5 	5L L L, , , , ,r2   r  c                       e Zd Zd Zej                            dddg          d             Zej                            dddg           fd            Zd Z	d	 Z
d
 Zej                            dg d          d             Z xZS )TestInvgaussc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestInvgauss.setup_method_
  r7  r2   zrvs_mu,rvs_loc,rvs_scale)rd   r   r   )g
ףp=@g r@gʡE6@c                    t           j                            d|||          }t           j                            ||          \  }}}||z
  }t	          j        |          }t          |          t	          j        |dz  |dz  z
            z  }	||	z  }
t          |
|dd           t          |	|dd           t          ||           t           j                            d|||          }t           j                            ||dz
  |dz             \  }}}t          |dz   |           t          |dz
  |           t           j                            |d	
          d         }t           j                            |d	          d         }t           j                            |d	          d         }||cxk    r|cxk    rd	k    sn J d S )Nr^   r   r  rb   rc   r   r   r   r   r   r>  r#  )fmur   )fix_mur   )
r6   r!  r   r   rg   r|  r  rn  r   r   )rp   rvs_mur   r   r   r  rb   rc   mu_temp	scale_mlemu_mle
shape_mle1
shape_mle2
shape_mle3s                 r0   r  zTestInvgauss.test_fitb
  s    ~!!sv&-Y " @ @ ++Dw+??Cg~'$--IIr
Wr](B!C!CD	" 	U;;;;	5u5AAAAS'"""~!!sv&-Y " @ @ ++Dw{3<q= , B BCY]E***Wq[#&&& ^''$'77:
^''T'::1=
^'''66q9
Z====:============r2   )gX9v>@g	@gGz@c                    t           j                            d|||          }t          t	          t           j                  t           j                  j        } ||          }t           j                            |          }t          ||            ||dd          }t           j                            |dd          }t          ||           t          t           j        ||           t          j	        ||dz
  z
  dk              sJ t          t           j        ||dz
             t          t           j        |d           t          t           j        ||t          j
                            d          d                    d S )	Nr^   r  r   rd   )r   r  r   r   r>  )r6   r!  r   r   r   r   r   r   rg   rB  r   rand)	rp   r   r   r   r   	super_fitsuper_fittedinvgauss_fit	__class__s	           r0   r   z(TestInvgauss.test_fit_MLE_comp_optimizer
  s|    ~!!sv&-Y " @ @ $u~..??C	 y~))$//\<000 !yA1555~))$QA)>>\<000 	&endIIII vtw{+q011111%end1MMMM 	&endCCCC 	&end-/Y^^A->->q-A	C 	C 	C 	C 	C 	Cr2   c                     t          t          j                   t          j        t
                    5  t          j                            g dd           d d d            d S # 1 swxY w Y   d S )Nr	  rd   r   )r  r6   r!  r   r   r!   r   ru   s    r0   test_fit_raise_errorsz"TestInvgauss.test_fit_raise_errors
  s    EN+++]<(( 	2 	2Nyyyq111	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2s   $A$$A(+A(c                    g d}g d}t           j                            d|          }t          ||           t           j                            dd          }t	          |d           t           j                            dd          }t	          |d	           t           j                            d
d          }t	          |d           t           j                            dd          }t	          |d           d S )N)g4wT;?gjdV&}?g{i\0>gDV_h?gqacX?)r   r   r   r   r   皙?r  r_  ?gfFn   gr^:g9̗?r  gx_;:g!?gٷ
??)r6   r!  rn   r   r   r  )rp   r  rU   rQ   
cdf_actual	sf_actuals         r0   ru  zTestInvgauss.test_cdf_sf
  s    . . ."??##CB#//Xv&&& ^''$'77

$9:::N%%cd%33		#7888 ##GV44 3444 ##Hf55 122222r2   c                    t           j                            dd          }t          |d           t           j                            dd          }t          |d           t           j                            dd          }t          |d           t           j                            dd          }t          |d	           d S )
Nr  r  r  giJ.r  gr^ߺr_  gpgFgpQ^L)r6   r!  r  r   rw  )rp   r  rw  s      r0   ry  zTestInvgauss.test_logcdf_logsf
  s     &&v$&77 1222&&sD11 5666$$Ut$445666$$S$//011111r2   zmu, ref))g:0yU>g,9)r_  g%!)r{   g40)r   gK'
@)r  g`p
@c                 d    t          t          j                            |          |d           d S r  )r   r6   r!  rE   )rp   r  r  s      r0   rr  zTestInvgauss.test_entropy
  s/     	..r22CeDDDDDDr2   )r   r   r   r6  r   r   r   r  r   r  ru  ry  rr  __classcell__r  s   @r0   r  r  ^
  s;          [7')>?A A> >A A>: [7')>?A AC C C CA ACB2 2 2!3 !3 !3F2 2 2. [Y )D )D )D E E
E EE E
E E E E Er2   r  c                       e Zd Zej                            dg d          ej                            dg d          d                         Zej                            dg d           fd            Zd	 Zd
 Z	d Z
d Z xZS )TestLaplacer   )r>  r   r   rd   r   )r   rd   r   r]   c                    t           j                            d||          }t          j        |          }t          j        t          j        ||z
                      t          |          z  }t           j                            |          \  }}t          ||dd           t          ||dd           t           j                            ||          \  }}t          ||dd           t           j                            ||          \  }}t          ||           |dz  }t          j        t          j        ||z
                      t          |          z  }t           j                            ||          \  }}t          ||           t           j                            ||          \  }}t          ||           t          t          t           j        j        |||           t          t          t           j        j        t          j        g           t          t          t           j        j        t          j        g           d S )	Nr^   r  r   r   r   r  rd   r>  )r6   r2  r   rg   r  rn  r   r  r   r   r   r?  r  r  r  r  )rp   r   r   r   loc_mler  rb   rc   s           r0   r  zTestLaplace.test_fit
  s   
 }  cwi HH )D//F26$.1122SYY>	 ]&&t,,
UW5u====yu5AAAA ]&&t'&::
Uyu5AAAA]&&tI&>>
UW%%% kF26$*--..T:	 ]&&t#&66
UY&&& ]&&tI&>>
UWc""" 	lEM$5t'&	( 	( 	( 	( 	j%-"3bfX>>>j%-"3bfX>>>>>r2   rvs_loc,rvs_scale))r>  r]   r]   r   )ry   r  c                    t           j                            d||          }d }t           j                            |          \  }}t	          t          t           j                  t           j                                      |          \  }} ||||          }	 ||||          }
|	|
k     st          j        |	|
dd          sJ d S d S )Nr   r  c           	          dt          |           t          j        d|z            z  d|z  t          j        t          j        || z
                      z  z
  z  S )Nr   rd   r   )r  rg   r  rn  r   )rb   rc   r   s      r0   llz3TestLaplace.test_fit_MLE_comp_optimizer.<locals>.ll"  sS    CII%8E'26"&*<*<#=#==> ? ?r2   r   r   )r6   r2  r   r   r   r   rg   r   )rp   r   r   r   r"  rb   rc   loc_opt	scale_optll_mlell_optr  s              r0   r   z'TestLaplace.test_fit_MLE_comp_optimizer  s     }  dy II	? 	? 	? ]&&t,,
U"4#6#6#(=2 225#d)) 	C%%GY--"+ff38u#F #F #Fr2   c                    t          j        g d          }t          j                            |d          \  }}t          |ddd           t          j                            |d          \  }}t          |ddd           d S )N)rU  rU  rV  rV         @r3  r  r   r   r   r   r  )rg   r   r6   r2  r   r   )rp   r   rb   rc   s       r0   test_fit_simple_non_random_dataz+TestLaplace.test_fit_simple_non_random_data0  s    x77788]&&t!&44
Uqu59999]&&tA&66
UQU777777r2   c                 F   d}t           j                            |           }|dk    sJ t           j                            |          }|dk    sJ t           j                            |          }|dk    sJ t           j                            |           }|dk    sJ d S )Nr   r~   rU  )r6   r2  rn   r  )rp   r\   p0p1s       r0   test_sf_cdf_extremesz TestLaplace.test_sf_cdf_extremes9  s    ]r"" Syyyy ]q!!Syyyy]a   Syyyy ]qb!!Syyyyyyr2   c                     d}t           j                            |          }t          |t	          j        |           dz  d           d S )Nr  rd   r   r   )r6   r2  r  r   rg   r   )rp   r\   rw  s      r0   r  zTestLaplace.test_sfN  sE    MQ261"::a<e444444r2   c                     d}t           j                            |          }t          |t	          j        d|z             d           d S )Ng}:rd   r   r   )r6   r2  r  r   rg   r  )rp   rw  r\   s      r0   r  zTestLaplace.test_isfS  sE    Ma  BF1Q3KK<e444444r2   )r   r   r   r   r   r   r  r   r)  r-  r  r  r  r  s   @r0   r  r  
  s       [Y66[[---88)? )? 98 76)?V [0 3? 3? 3? @ @F F F F@ @F$8 8 8  *5 5 5
5 5 5 5 5 5 5r2   r  c                      e Zd Zej                            dddg          d             Z ej        d          d             Zej                            dg d	          ej                            d
g d          ej                            dg d          ej                            dd  e	ddgd          D                       d                                                 Z
d Zd Zd ZdS )TestPowerlawzx, a, sf)r   r}   g      ?)g     ?g      p?gSQ>c                 f    t          t          j                            ||          |d           d S r   )r   r6   powerlawr  )rp   r\   r.   r  s       r0   r  zTestPowerlaw.test_sf\  s1     	))!Q//%@@@@@@r2   r  r  c                 @    t           j                            d          S r3  r	  ru   s    r0   r   zTestPowerlaw.rngb  r
  r2   r   )rZ   ry   rc  r   rd   r   r  r   r  r.  c                     g | ]}d |v |	S r0  r8   r1  s     r0   r@   zTestPowerlaw.<listcomp>j  r2  r2   TFr   r3  c                 $   t           j                            d||||          }t                      }	|r||	d<   |r5t	          j        |                                t          j                   |	d<   |r||	d<   t          t           j        |fi |	 d S )Nr  )r   r.   rb   rc   r   r   r   r   )	r6   r3  r   r  rg   	nextafterr  r  r   r9  s
             r0   r   z(TestPowerlaw.test_fit_MLE_comp_optimizerf  s     ~!!siW(1 " E E vv 	#"DJ 	=<

RVG<<DL 	'&DN%endCCdCCCCCr2   c           	          d}d}d}t           j                            |||dt          j                            d                    }d|                                dz  i}t          t           j        |fi | d S )	Ng`- @r~   grߟA@r^   r   )r.   rb   rc   r   r   r   rd   )r6   r3  r   rg   r   r   ptpr   )rp   r.   r;  rc   r   r   s         r0   test_problem_casezTestPowerlaw.test_problem_casez  s     #"~!!A85s/1y/D/DQ/G/G " I I $((**q.)%endCCdCCCCCr2   c                 z   t          t          j                   d}t          t          |          5  t          j                            g ddd           d d d            n# 1 swxY w Y   d}t          t          |          5  t          j                            g dd           d d d            n# 1 swxY w Y   d}t          t          |          5  t          j                            g dd	           d d d            n# 1 swxY w Y   d
}t          t          |          5  t          j                            g dd           d d d            n# 1 swxY w Y   d}t          t          |          5  t          j                            g dd           d d d            d S # 1 swxY w Y   d S )Nz7 Maximum likelihood estimation with 'powerlaw' requiresr  r   rd   r   r   r   r>  rd   r   r   z$Negative or zero `fscale` is outsider  r  z0`fscale` must be greater than the range of data.)r  r6   r3  r?  r!   r   r  )rp   r,   s     r0   r@  zTestPowerlaw.test_fit_warnings  s   EN+++H<s333 	< 	<Nyyyq;;;	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< I<s333 	2 	2Nyyyq111	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 I<s333 	2 	2Nyyyq111	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 6:S111 	5 	5Nyyy444	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 B:S111 	4 	4Nyyy333	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4sY   %A##A'*A'$B66B:=B:$D		DD,$EE #E ?$F00F47F4c                     g d}t           j        }t          j        d          5  t	          ||           d d d            d S # 1 swxY w Y   d S )N)r   r   rd   rd   r   r   r   r   r   r   r   r  r5  over)r6   r3  rg   rD  r   )rp   r   r?   s      r0   test_minimum_data_zero_gh17801z+TestPowerlaw.test_minimum_data_zero_gh17801  s     433~[h''' 	6 	6)$555	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6s   AAAN)r   r   r   r   r   r   r  r  r   r%   r   r:  r@  r@  r8   r2   r0   r1  r1  Y  s~        [Z1HJK KA AK KA V^*%%%+ + &%+ [[*=*=*=>>[Y


33[[***55[<- -$q)I)I)I - - -. .D D. . 65 43 ?>DD D D4 4 466 6 6 6 6r2   r1  c                   >   e Zd Zej                            dg d          d             Zej                            dddg          d             Zej                            dg d          d	             Zej                            dg d
          d             Z	dS )TestPowerLogNormzx, c, s, ref))r^   r  r   ga!R()r_  r  r   g;?)r_  ri  r   gE?)MDri  r   g=c                 h    t          t          j                            |||          |d           d S r   )r   r6   r(  r  rp   r\   r  rL   r  s        r0   r  zTestPowerLogNorm.test_sf  s4     	*--aA66%HHHHHHr2   zq, c, s, ref)g?ri  r   r{   )gR4-r  r   r   c                 h    t          t          j                            |||          |d           d S )Ng|=r   )r   r6   r(  r  )rp   r  r  rL   r  s        r0   r  zTestPowerLogNorm.test_isf  s4     	*..q!Q775IIIIIIr2   ))(,* Eri  r   g?)r  ri  r   gv6)r  r  r   g+	94|7)r  r  r   g?c                 h    t          t          j                            |||          |d           d S )Ngt =r   )r   r6   r(  rn   rE  s        r0   r]  zTestPowerLogNorm.test_cdf  s4     	*..q!Q775IIIIIIr2   ))rC  ri  r   gS^Ռe9)@xDr_  r   g0g;)g\)c=Hr_  r   g7H7c                 h    t          t          j                            |||          |d           d S )NgAfc=r   )r   r6   r(  rf   rE  s        r0   rS  zTestPowerLogNorm.test_pdf  s4    
 	*..q!Q775IIIIIIr2   N)
r   r   r   r   r   r   r  r  r]  rS  r8   r2   r0   rB  rB    s<       " [^E E EF F
I IF F
I
 [^ACEF FJ JF FJ [^A A AB B
J JB B
J [^G G GH HJ J	H HJ J Jr2   rB  c                       e Zd Zej                            dg d          d             Zej                            dg d          d             Zej                            dg d          d             Zd	S )
TestPowerNormr  ))rQ  r   g| <)r  rd   ge()r^   ri  g%!@6)r  r{   gT;-c                 f    t          t          j                            ||          |d           d S r   )r   r6   	powernormr  r  s       r0   r  zTestPowerNorm.test_sf  s1     	**1a00#EBBBBBBr2   rc  ))r  r  gĿ)gwJ?r^   g!X)r  ri  g缂U)r   ri  gͫ1@)r  rd   gD@)Jz5r   gU!zYr@c                 f    t          t          j                            ||          |d           d S Nr  r   )r   r6   rN  r  rf  s       r0   r  zTestPowerNorm.test_isf   s1     	++Aq113UCCCCCCr2   ))irQ  g.u	T9)rd   rQ  ?)r  rQ  gsK-)r>  ri  gk8>)r  ri  g^u1-c                 f    t          t          j                            ||          |d           d S r  )r   r6   rN  rn   r  s       r0   r]  zTestPowerNorm.test_cdf  s1     	++Aq113UCCCCCCr2   N)	r   r   r   r   r   r   r  r  r]  r8   r2   r0   rL  rL    s         [[C C CD D
C CD D
C [[= = => >D D> >D [[B B BC CD DC CD D Dr2   rL  c                   l    e Zd Zd Zd Zd Zej                            dddg          d             Z	dS )	TestInvGammac                    t          j                    5  t          j        dt                     t          j                            dd          }g d}t          ||           g d}t          j                            |d          }g dt          j        dd	gt          j	        d
dgt          j	        t          j	        dgf}t          ||          D ]\  }}t          ||           	 d d d            d S # 1 swxY w Y   d S )Nrt  g(\O3@rW  r  )g~?gCX&?g*7gS?gBqFq @)皙?@gffffff@)r  gEy?gў3oz?g^Yb?g,r?gOD@g2*Z@gFN8@)rx  ry  rz  r{  r6   r   r   rg   r  r  r  r   )rp   rW  rU   r.   r\   r  s         r0   test_invgamma_inf_gh_1866z&TestInvGamma.test_invgamma_inf_gh_1866  sU    $&& 	* 	*!'>:::>''%'@@D% % %HD(+++A>''!V'<<D888}=k:57H D(++ * *1#Aq))))*	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	*s   CC66C:=C:c                     t          j        dd          }t          j                            |d          }t          j                            |d          }t          ||           d S )Ngr   r   )rg   r  r6   r   rn   r  r   r  s       r0   r  zTestInvGamma.test_cdf_ppf/  sW    Ka  Nq!$$^1%%2r2   c                     t           j        dk    rt          j        dd          }nt          j        dd          }t          j                            |d          }t          j                            |d          }t          ||d           d S )N        rd   r^      r   rU  r   )	sysmaxsizerg   r  r6   r   r  r  r   r  s       r0   r  zTestInvGamma.test_sf_isf6  s~    ;As##AA Ar""ANa##^1%%2C((((((r2   a, ref)r   g70K6:)r  gVMOuc                 d    t          t          j                            |          |d           d S r   )r   r6   r   rE   rp   r.   r  s      r0   test_large_entropyzTestInvGamma.test_large_entropyC  s/     	..q113UCCCCCCr2   N)
r   r   r   rY  r  r  r   r   r   rc  r8   r2   r0   rU  rU    s        * * *&  ) ) ) [X?:<= =	D 	D= =	D 	D 	Dr2   rU  c                   &    e Zd Zd Zd Zd Zd ZdS )TestFc                     t           j        ddgg}|D ]\  }}} |j        |j        g|R  }d |D             }d |D             }t	          ||           d S )N)rd   r   rU  c                 <    g | ]\  }}} |j         |j        g|R  S r8   rf   r.   r>   _f_argsr   s       r0   r@   z(TestF.test_endpoints.<locals>.<listcomp>Y  4    ===E1vrvbd#U###===r2   c                     g | ]\  }}}|	S r8   r8   r>   rj  rk  	_correct_s       r0   r@   z(TestF.test_endpoints.<locals>.<listcomp>Z      >>>!5UI9>>>r2   )r6   frf   r.   r   )rp   r   rj  rk  _correctanscorrects          r0   r  zTestF.test_endpointsS  s    &#&'#' 	' 	'Bx"&&&&&CC=====>>>>>!#w/////r2   c                 ^   t           j                             ddd          \  }}}}t          t          j        |                     t          t          j        |                     t          t          j        |                     t          t          j        |                      d S )Nr        @rW  rX  )r6   rq  r	   rg   r  r  s        r0   test_f_momentszTestF.test_f_moments]  s    W]]2sF];;
1aAAABKNN"#####r2   c                     t          j                    5  t          j        dt                     t          j                            dgdz  g dd           d d d            d S # 1 swxY w Y   d S )Nrt  r  r   )rd   r   r  r?  rW  dfndfdrY  )rx  ry  rz  r{  r6   rq  ru   s    r0   test_moments_warningszTestF.test_moments_warningse  s    $&& 	H 	H!'>:::GMMrd1f,,,MGGG	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	Hs   AA$$A(+A(c                    t          j        dgdgg          }t          j        ddg          }t          j                            ||d          \  }}}}||dz
  z  gdz  }t	          ||           d|dz  z  ||z   dz
  z  |z  |dz
  dz  z  |dz
  z  }t	          ||           d|z  |z   dz
  t          j        d|dz
  z            z  |d	z
  t          j        |||z   dz
  z            z  z  }	t	          ||	           d|d
|z  dz
  z  ||z   dz
  z  |dz
  |dz
  dz  z  z   z  }
||d	z
  z  |dz
  z  ||z   dz
  z  }|
|z  }t	          ||           d S )Nr   r  rW  rW  ry  rd   r   r?  r  r      )rg   r   r6   rq  r   r)  )rp   rz  r{  r@  rA  rL   rY   r  v2s2k2numk2denk2s                r0   test_stats_broadcastzTestF.test_stats_broadcastk  s   hbT{##hBx  W]]sV]DD
1aS1Woq 2aZ39q=)C/37Q,>#'J2us{Q"'!S1W+"6"66a273c	A#677792cQsURZ(C#IM:Qw37Q,./ 0sQw37+sSy1}=U]2r2   N)r   r   r   r  rw  r|  r  r8   r2   r0   re  re  R  sS        0 0 0$ $ $H H H    r2   re  c                      e Zd Zd Zd Zd Zej                            dddg          d             Z	ej                            dg d	          ej                            d
ddgddgddgg dg dgddgddggdgdggg          d                         Z
ej                            d
ddgddgddgg dg dgddgddggdgdggg          d             Zd ZdS )TestStudentTc                 h    t          t          j                            ddg          ddg           d S )Nr   r  g?g?)r   r6   r+  r}  ru   s    r0   test_rvgeneric_stdzTestStudentT.test_rvgeneric_std~  s/    !%'++q!f"5"5
J7OPPPPPr2   c                 b   t          t          j                            dd          t          j        t          j        t          j        t          j        f           t          t          j                            dd          dt          j        t          j        t          j        f           t          t          j                            dd          dt          j        t          j        t          j        f           t          t          j                            dd          ddt          j        t          j        f           t          t          j                            d	d
          t          j        t          j        f           t          t          j                            dd
          dt          j        f           t          t          j                            dd
          dt          j        f           t          t          j                            dd
          d           d S )Nr   rW  )r  rY  )\(?r~   rd   gGz @g     i@r   r  gGz@r   g
ףp=
@)r~   gq    @)r   r6   r+  rg   r  r  ru   s    r0   test_moments_tzTestStudentT.test_moments_t  s   UW]]a]88VRVRVRV4	6 	6 	6UW]]dF];;"&"&"&1	3 	3 	3UW]]a]88"&"&"&1	3 	3 	3UW]]dF];;/2626:	< 	< 	<UW]]a]668HIIIUW]]dD]99C=IIIUW]]a]66bfFFFUW]]dD]99;RSSSSSr2   c                 t    g d}g d}t          t          j                            |          |d           d S )N)r   rd   r  r^   )g?@gTM]?ggY?U?r   r   r   r6   r+  rE   )rp   r  rU   s      r0   test_t_entropyzTestStudentT.test_t_entropy  sE    __; ; ;++XEBBBBBBr2   zv, ref)r^   r  )r  r  c                 d    t          t          j                            |          |d           d S r  r  )rp   rA  r  s      r0   test_t_extreme_entropyz#TestStudentT.test_t_extreme_entropy  s-     	**Ce<<<<<<r2   methname)rf   r   rn   r  r  r  
df_infmaskr   r   )r   r   r   )r   r   r   c                    t           j                            d           t          j        |t                    }t           j                            dd|j                  }t          j        j        |j         }t           j        ||<   t          j
        |dd          }t          j
        ||          dd          }t          j        dd          }t          ||          }t          ||          }	t          ||          }
 ||          }t          ||          |
||                              t          ||           |	||                               d S )	Nr   r   r]   r:  r   r   r  rb   rc   ra   )rg   r   r   r   boolrT  rC  randnr  r6   r+  r  r,  r   )rp   r  r  r  r\   t_dist
t_dist_ref	norm_distt_meth
t_meth_ref	norm_methr   s               r0   test_t_inf_dfzTestStudentT.test_t_inf_df  s6    		qZ
$777
Yq":+;<<IOZ-.:BAQ///WJ;Qa@@@
J1A...	**Z22
Ix00	fQiiS_ii*&>&>???S*%zz!ZK.'A'ABBBBBr2   c                    t           j                            d           t          j        |t                    }t           j                            dd|j                  }t           j        ||<   t          j	                            |ddd          }t          j
                            ddd	          }t          j	                            ||          ddd          }t          d
          D ]G}t          ||         |         ||                    t          ||         |          ||                    Ht          j	                            |dd          }t          j
                            dd          }t          j	                            ||          dd          }t          ||         |           t          ||          |           d S )Nr   r  r]   r:  r   r   rW  )r  rb   rc   rY  rb   rc   rY  r   r  ra   )rg   r   r   r   r  rT  rC  r  r6   r+  r  r   r   rE   )rp   r  r  r   
res_ex_infres_ex_noinfr  s          r0   test_t_inf_df_stats_entropyz(TestStudentT.test_t_inf_df_stats_entropy  s   
 		qZ
$777
Yq":+;<<:gmmrq6mBBZ%%!1f%EE
w}}J;Qa,2 % 4 4q 	? 	?AQ
+Z];;;Q,l1o>>>>goo!o44Z''AQ'77
w"j[/qJJS_j111S*%|44444r2   c                     g d}g d}g d}g d}t          t          j                            ||          |d           t          t          j                            ||          |d           d S )N)r   r  r]   r   )r  d~QJrI  r   )gZ_2g9g!ǟuIgdg)g73?r   gմFhAW;gm0_?r   r   r~  )r   r6   r+  r   rf   )rp   r\   r  
logpdf_refpdf_refs        r0   test_logpdf_pdfzTestStudentT.test_logpdf_pdf  s     OO###@ @ @
> > >q"--zFFFFAr**G%@@@@@@r2   N)r   r   r   r  r  r  r   r   r   r  r  r  r  r8   r2   r0   r  r  }  s       Q Q QT T TC C C [X68:; ;= =; ;= [Z *< *< *< = =[\QFQFQF-6YY			,B./VaV,<./S1#J,8 9 9C C	9 9= =C  [\QFQFQF-6YY			,B./VaV,<./S1#J,8 9 95 5	9 95(
A 
A 
A 
A 
Ar2   r  c                   V    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd ZdS )TestRvDiscretec                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestRvDiscrete.setup_method  r7  r2   c           	         g d}g d}d}t          j        d||f          }|                    |          }t          t	          |t
          j                             t          ||          D ]I\  }}t          t          t          ||k              t          |          z  |z
            dk                J|                                }t          j        t          |          t          j                  sJ d S )N)r   r   r   rd   r   r   )r~   r  r  r~   r  r~   r   sample)namevaluesr:  r   )r6   rB   r   r	   rE  rA  rf  r  r   rn  r   rg   r   r   integer)rp   statesprobabilitysamplesr  r\   rL   rw  s           r0   rK  zTestRvDiscrete.test_rvs  s    $$$4448V[4IJJJEEwE
1em,,---,, 	@ 	@DAqCAFE'NN2Q677$>????EEGG}T!WWbj1111111r2   c                 f   t          j        g d          }t          j        g d|f          }t	          t          ||                     }|                                }t          ||           t          j        g dg df          }|                                }t          |d           d S )N)r   r  r  r  r  )rU  r   r   r~   )	rg   r   r6   rB   rn  r   rE   r   r   )rp   r'  rw  rp  rq  s        r0   rr  zTestRvDiscrete.test_entropy  s    ***++iii%7888%u--...
IIKK:&&&iii%=>>>IIKKQr2   c                     g d}g d}t          j        ||f          }ddgddgg}t          |                    |          dd	gd
dggd           d S )Nr<  ry   r  r  r  rU  r  rV  rd   ry   r  r~   r  r~  r   )r6   rB   r   rQ  )rp   xkpkrQ  r\   s        r0   rl  zTestRvDiscrete.test_pmf  s    YY__r2h///"X!Wq		sc$*/	1 	1 	1 	1 	1 	1r2   c                     g d}g d}t          j        ||f          g d}g d}t                              |          |d           t          fd|D             |d           d S )	Nr<  r  r  )r   rU  rW  r  r}   rV  r   r   )r   ry   ry   ry   r  r  r   r   r~  r   c                 :    g | ]}                     |          S r8   )rn   )r>   r  rQ  s     r0   r@   z+TestRvDiscrete.test_cdf.<locals>.<listcomp>  s#    777777r2   )r6   rB   r   rn   )rp   r  r  x_valuesrU   rQ  s        @r0   r]  zTestRvDiscrete.test_cdf  s    YY__r2h///555555x(((???? 	7777h777 u	. 	. 	. 	. 	. 	.r2   c                     g d}g d}t          j        ||f          g d}g d}t                              |          |d           t          fd|D             |d           d S )	Nr<  r  r  )rZ   ry   r  r  r  rU  )r   r   rd   rd   r   r   r~  r   c                 :    g | ]}                     |          S r8   )r  )r>   r  rQ  s     r0   r@   z+TestRvDiscrete.test_ppf.<locals>.<listcomp>$  s#    555q555r2   )r6   rB   r   r  )rp   r  r  q_valuesrU   rQ  s        @r0   r`  zTestRvDiscrete.test_ppf  s    YY__r2h///000%%%x(((???? 	5555H555 u	. 	. 	. 	. 	. 	.r2   c           	          g dg df}t          j        |          }t          |                    |                    |j        d d                   dz             |j        dd                     d S )N)r   rd   r   r  r?  )rZ   r  r  r  rZ   r  r   r  r   )r6   rB   r   r  rn   r  )rp   rI  rQ  s      r0   test_cdf_ppf_nextz TestRvDiscrete.test_cdf_ppf_next'  s|    !:!:!:;d+++266"&&ss"4"4t";<<59	& 	& 	& 	& 	&r2   c                 B   t          j        d                              d          }t          j        g dg dg dg          }t	          j        ||f          }t          |                                t          j        |j	        |j
        z            d           d S )NrW  )r   r   )rZ   rZ   r  r   )rZ   rZ   r   r   r  r~  r   )rg   r  r  r   r6   rB   r   r   rn  r  r  rp   r  r  rQ  s       r0   test_multidimensionz"TestRvDiscrete.test_multidimension/  s    Yr]]""6**X---------/ 0 0 r2h///		RVBEBEM%:%:GGGGGGr2   c                    g d}ddg}t          t          t          j        fi t	          ||f           g d}t          t          t          j        fi t	          ||f           g d}g d}t          t          t          j        fi t	          ||f           g d}g d}t          t          t          j        fi t	          ||f           d S )Nr	  ry   r  )ry   333333?gffffff濩r   rd   r   r   r   )r  r  r  r  r  )r?  r  r6   rB   r  rp   r  r  s      r0   test_bad_inputzTestRvDiscrete.test_bad_input8  s    YY3Zj%"3MMtB87L7L7LMMMYYj%"3MMtB87L7L7LMMMYYj%"3MMtB87L7L7LMMM__'''j%"3MMtB87L7L7LMMMMMr2   c                    t          j        d                              d          t          j        dd          }}t	          t
          t          j        fi t          ||f           t          j        d                              d          t          j        dd          }}t	          t
          t          j        fi t          ||f           t          j        d                              d          t          j        dd          }}t          t          j        ||f          
                    d          d           d S )	Nr   rd   rd   )rd   r   gUUUUUU?r  r  r   rd   r   )rg   r  r  r  r?  r  r6   rB   r  r   rQ  r  s      r0   test_shape_rv_samplez#TestRvDiscrete.test_shape_rv_sampleH  s    1%%f--rwvs/C/CBj%"3MMtB87L7L7LMMM 1%%f--rwvs/C/CBj%"3MMtB87L7L7LMMM 1%%f--rwvs/C/CBU&r2h777;;A>>DDDDDr2   c                     g d}g d}t          j        ||f          }t          |                                t	          j        |j        |j        z            d           d S )N)r   rd   r   r  r  r  )rZ   r  r  r  r  rZ   r  r~  r   )r6   rB   r   r   rg   rn  r  r  r  s       r0   test_expect1zTestRvDiscrete.test_expect1W  sd       +++r2h///		RVBEBEM%:%:GGGGGGr2   c           
         g d}g d}t          j        ||f          }t          |                                |                                d           t          |                                t          d t          ||          D                       d           t          |                    d           t          d t          ||          D                       d           d S )	N)/g      i@g     r@g      y@g     @@g     @g     @      @g      @r  g     0@g     @g     P@g     @g     p@g      @g     @g      @g     @r  g     h@g     0@g     @g     @g     @g     P@g     @g     @g     @r  g     8@g      @g     ȩ@g     @g     X@g      @g     @g     @g     x@g     @@g     @g     h@g     ̰@g     0@g     @g     @g     \@g     @)/g-C6:?r~   gF%uk?g:vz?r~   r~   g.nr?g|гY?r~   r~   r~   g @6*? 4U0*C?g@+?gC6z?g nr?g ?gOjM?g n?g1w-!?g:pΈ?gףp=
?g _Le?r~   g^)p?g~jtx?gJ4q?gGzt?g J4q?g Mb@?g@Psׂ?g@^)ˀ?r~   r~   g N@s?g 1w-!_?r  gൄ|г?r~   gH}}?r~   g
F%u?r~   r~   g ^)ˀ?g v?r~   r  r~  r   c              3   &   K   | ]\  }}||z  V  d S rs   r8   r>   rA  ws      r0   	<genexpr>z.TestRvDiscrete.test_expect2.<locals>.<genexpr>}  s*      99daAE999999r2   c                     | dz  S Nrd   r8   r   s    r0   rM   z-TestRvDiscrete.test_expect2.<locals>.<lambda>  
    AqD r2   c              3   ,   K   | ]\  }}|d z  |z  V  dS )rd   Nr8   r  s      r0   r  z.TestRvDiscrete.test_expect2.<locals>.<genexpr>  s.      <<AAqD1H<<<<<<r2   )r6   rB   r   r   r|  rn  r  )rp   r  pyrQ  s       r0   test_expect2zTestRvDiscrete.test_expect2^  s
   = = =? ? ?  q"g... 			RWWYYU;;;;		99c!Rjj99999	G 	G 	G 	G 			..11<<Q<<<<<5	J 	J 	J 	J 	J 	Jr2   N)r   r   r   r6  rK  rr  rl  r]  r`  r  r  r  r  r  r  r8   r2   r0   r  r    s          2 2 2
 
 
	1 	1 	1. . .. . .& & &H H HN N N E E EH H H#J #J #J #J #Jr2   r  c                       e Zd Zd Zd ZdS )TestSkewCauchyc                    t          j        ddd          }t          t          j                            |d          t          j                            |                     t          t          j                            |d          t          j                            |                     t          t          j                            |d          t          j                            |                     d S Nr>  r   r^   r   r  )	rg   rZ  r   r6   
skewcauchyrf   r.  rn   r  r  s     r0   test_cauchyzTestSkewCauchy.test_cauchy  s    KAs##!%"2"6"6qA"6">">"',"2"21"5"5	7 	7 	7!%"2"6"6qA"6">">"',"2"21"5"5	7 	7 	7!%"2"6"6qA"6">">"',"2"21"5"5	7 	7 	7 	7 	7r2   c                    t           j                            d           t           j                            d          dz  dz
  }t           j                            d          dz  dz
  }g d}g d}t	          t
          j                            ||          |           t	          t
          j                            ||          |           t	          t
          j        	                    ||          |           d S )Nr   r]   rd   r   r   )
g& 45?gQʶ?g-4<??gJ?gw@v?gJ%?g>[u?g
a2?g	Rn?gѦ}cي?)
gN@Q?gPPz@	?g?g;
7?glg?g!?%?gQҙ?gC"?go?g@Sg?)
rg   r   r   r  r   r6   r  rf   rn   r  )rp   r.   r\   rf   rn   s        r0   test_skewcauchy_Rz TestSkewCauchy.test_skewcauchy_R  s    & 		qINN2"Q&INN2#a'% % %$ $ $ 	(,,Q22C888(,,Q22C888(,,S!44a88888r2   N)r   r   r   r  r  r8   r2   r0   r  r    s2        7 7 7 9  9  9  9  9r2   r  rd   r   g@r   gףp=
1@r>  gRZ@i   gS㥛Ԋ@rZ   r[   g&@iQ i'  i0ybi l   HO1Z i3r  ir]   ir^   ikr  i1r   i  i4i N  i(  lEI. @ i c                       e Zd Zd Zd Zd Zd Zd Zd Ze	j
                            de          d             Zd	 Zd
S )TestSkewNormc                 .    t          d          | _        d S r3  )r   r   ru   s    r0   r6  zTestSkewNorm.setup_method  s    %d++r2   c                     t          j        ddd          }t          t          j                            |d          t          j                            |                     d S r  )rg   rZ  r   r6   skewnormrf   r  r  s     r0   test_normalzTestSkewNorm.test_normal  sY    KAs##!%."4"4Q!"4"<"<"'*.."3"3	5 	5 	5 	5 	5r2   c                     d}t           j                            d|| j                  }t	          ||j                   t           j                            d|| j                  }t	          ||j                   d S )N)r   r   r   rc  )r.   r   r   r  )r6   r  r   r   r   rC  )rp   rC  r\   s      r0   rK  zTestSkewNorm.test_rvs  sm    NEIIUAG$$$N%dhGGUAG$$$$$r2   c                    t           j                            dt          d          dd| j                  }t          j        |          t          j        |          t          j        |          t          j	        |          g}t           j                             dddd          }t          ||d           t           j                            d	t          d          dd| j                  }t          j        |          t          j        |          t          j        |          t          j	        |          g}t           j                             d	ddd          }t          ||d           d S )
Nr   r  r   rd   )r.   r   rb   rc   r   rW  )r.   rb   rc   rY  rX  r  )r6   r  r   re  r   rg   r|  r  r  kurtosisr   )rp   XrU   r  s       r0   rB  zTestSkewNorm.test_moments  s,   NSq,0H  6 6GAJJq		5:a==%.:K:KL>''!!V'LL!(Ha@@@@N#c((,0H  6 6GAJJq		5:a==%.:K:KL>''"!1f'MM!(Ha@@@@@@r2   c                     t           j                            g dd          }t          |t	          j        d          d           t           j                            dd          }t          |dd           d S )	N)r]   r  r9  r   r   r~  r   r  r  rU  )r6   r  rn   r   rg   onesr  s     r0   test_cdf_large_xzTestSkewNorm.test_cdf_large_x  sn     N|||R00271::E2222Nr3''3U++++++r2   c                    g dg dg dg dg dg}|D ]l\  }}}t           j                            ||          }t          ||d           t           j                            | |           }t          ||d           md S )N)rO  r   gzbLe9)r  rd   gn'/2;)r   r   g::)r8  r   g|<)r  r  r  r  r   )r6   r  rn   r   r  )rp   cdfvalsr\   r.   cdfvalrw  s         r0   test_cdf_sf_small_valuesz%TestSkewNorm.test_cdf_sf_small_values  s     .--+++,,,...///
 $ 	2 	2LAq&""1a((AAvD1111!!1"qb))AAvD11111	2 	2r2   z
a, momentsc                     t          |d          D ]7\  }}t          j                            ||          }t	          ||d           8d S )Nr   )startr~  r   )r  r6   r  r  r   )rp   r.   rY  orderrU   moms         r0   test_noncentral_momentsz$TestSkewNorm.test_noncentral_moments  s[    (::: 	7 	7OE8.''q11CC66666	7 	7r2   c           	         t           j                            d          }d\  }}}t          j        |||          }|                    d|          }t          j                            |dd          \  }}}	t          j                            |dd          \  }
}}||cxk    rdk    sn J ||
k    sJ t          j                            |ddd	
          \  }}}|dk    sJ t          j        |||          }|                    d          }t          j        |          t          j        |          f}t          ||           t          j
                            dd|          }t          j                            |          }t          j        t          j        |                    sJ t          j                            |d	          \  }}}t          j        |          sJ t          j        |          t          j        |          }}t          |||t          j        dt           j        z            z  z              t          ||dz  ddt           j        z  z
  z             d S )Nl   #ke )r   r  ry   r^   r  r  r   r   gmmr   methodmsrX  r   r  rd   )rg   r   r   r6   r  r   r   r|  r  r   r  rB  r  isinfr  r)  rh   )rp   r   r.   rb   rc   r?   r   a2loc2scale2a3loc3scale3a4loc4scale4dist4r   r  a5loc5scale5r@  rA  s                           r0   r  zTestSkewNorm.test_fit  sC   i##$788$3~ae,,hhCch22 !>--c4a-@@D& >--c4a-@@D&t    q      Rxxxx !>--c1Qt-LLD&{{{{r400kk$k''gcllEJsOO+S!!! lqs== n  %%vbk#&&''''' !>--c$-??D&x|| ws||RVC[[14&271RU7+;+;";;<<<619AI677777r2   N)r   r   r   r6  r  rK  rB  r  r  r   r   r   _skewnorm_noncentral_momentsr  r  r8   r2   r0   r  r    s        , , ,5 5 5% % %A A A, , ,2 2 2" [\+GHH7 7 IH7
&8 &8 &8 &8 &8r2   r  c                   &    e Zd Zd Zd Zd Zd ZdS )	TestExponc                 `    t          t          j                            d          d           d S r  )r   r6   r  rf   ru   s    r0   	test_zerozTestExpon.test_zeroE  s&    U[__Q''+++++r2   c                     t          t          j                            d          d           t          t          j                            t          j                            d                    d           d S )Nr  r  )r   r6   r  rn   r  r  ru   s    r0   	test_tailzTestExpon.test_tailH  sR    U[__U++U333U[__U[^^B%7%788"=====r2   c                     t          j        dddddt           j        g          }t          t          t
          j        j        |           d S No_?46@yX5ͻ@j+?UX@)rg   r   r  r?  r  r6   r  r   r  s     r0   test_nan_raises_errorzTestExpon.test_nan_raises_errorL  <    HfffffbfEFFj%+/155555r2   c                     t          j        dddddt           j        g          }t          t          t
          j        j        |           d S r  )rg   r   r  r?  r  r6   r  r   r  s     r0   test_inf_raises_errorzTestExpon.test_inf_raises_errorQ  r!  r2   N)r   r   r   r  r  r   r#  r8   r2   r0   r  r  D  sP        , , ,> > >6 6 6
6 6 6 6 6r2   r  c                   l    e Zd Zd Zd Zd Zej                            dddg          d             Z	dS )	TestNormc                     t          j        dddddt           j        g          }t          t          t
          j        j        |           d S r  )rg   r   r  r?  r  r6   r  r   r  s     r0   r   zTestNorm.test_nan_raises_errorX  <    HfffffbfEFFj%*.!44444r2   c                     t          j        dddddt           j        g          }t          t          t
          j        j        |           d S r  )rg   r   r  r?  r  r6   r  r   r  s     r0   r#  zTestNorm.test_inf_raises_error]  r'  r2   c                 \    g d}t          t          t          j        j        |d           d S )Nr	  shrimp)plate)r?  r  r6   r  r   r  s     r0   test_bad_keyword_argzTestNorm.test_bad_keyword_argb  s,    IIi(CCCCCCr2   rb   r   r   c                     d}t           j                            d|z   d|z   |          }t          ||d           t           j                            d|z    d|z    |           }t          ||d           d S )Ngg	{F.:r  rW  rb   r   r   )r6   r  
_delta_cdfr   )rp   rb   rU   r  s       r0   test_delta_cdfzTestNorm.test_delta_cdff  s     )
%%bfbf#%>>xe4444
%%3i2c6%EExe444444r2   N)
r   r   r   r   r#  r,  r   r   r   r0  r8   r2   r0   r%  r%  W  sv        5 5 5
5 5 5
D D D [UQF++
5 
5 ,+
5 
5 
5r2   r%  c                       e Zd ZdZd Zd ZdS )TestUniformgh-10300c                     t          j        dddddt           j        g          }t          t          t
          j        j        |           d S r  )rg   r   r  r?  r  r6   rT  r   r  s     r0   r   z!TestUniform.test_nan_raises_errorv  =    HfffffbfEFFj%-"3Q77777r2   c                     t          j        dddddt           j        g          }t          t          t
          j        j        |           d S r  )rg   r   r  r?  r  r6   rT  r   r  s     r0   r#  z!TestUniform.test_inf_raises_error{  r5  r2   N)r   r   r   __doc__r   r#  r8   r2   r0   r2  r2  t  s7        N8 8 8
8 8 8 8 8r2   r2  c            
       D   e Zd Zd Zd Zd Zd Zej        	                    dg d          d             Z
ej        	                    dg d	g d
g dg dg dg          d             Zej        	                    dg dg dg dg dg dg dg          d             ZdS )TestExponNormc                 l   d }d\  }}}d||z  z  }t           j                             |||d          }t          | ||||                     d\  }}}d||z  z  }t           j                             |||d          }t          | ||||                     d\  }}}d||z  z  }t           j                             |||d          }t          | ||||                     d\  }}}d||z  z  }t           j                             |||d          }t          | ||||                     d S )	Nc                     dd| |z  dz  z  z   }d| |z  dz  z  |dz  z  }dd| |z  dz  z   dz  z  }|d| z  z   ||z  d| | z  z  z   ||gS )NrU  r   rd   r   r        @r   r8   )lamsigr  opK2exp_skewexp_kurts         r0   get_momsz,TestExponNorm.test_moments.<locals>.get_moms  sz     c#g\))DC#I>)D4L8Ha39q.0B77H3JC#s3w- 78LLr2   )r   r   r   rU  rW  r  )r  rd   rZ   )r   r   r   )r>  r  r  )r6   	exponnormr   )rp   rB  r  r>  r=  Kstss          r0   rB  zTestExponNorm.test_moments  sp   	M 	M 	M C39o##A2S&#IIC#sB!7!7888!C39o##A2S&#IIC#sB!7!7888C39o##A2S&#IIC#sB!7!7888"C39o##A2S&#IIC#sB!7!788888r2   c                     t          j        dddddt           j        g          }t          t          t
          j        j        |dd           d S 	Nr  r  r  r  r  r   r   r>  )rg   r   r  r?  r  r6   rC  r   r  s     r0   r   z#TestExponNorm.test_nan_raises_error  D    HfffffbfEFFj%/"5qqKKKKKKr2   c                     t          j        dddddt           j        g          }t          t          t
          j        j        |dd           d S rG  )rg   r   r  r?  r  r6   rC  r   r  s     r0   r#  z#TestExponNorm.test_inf_raises_error  rH  r2   c                 v   t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           d S )Ni|r   r~     r{   )r   r6   rC  rf   ru   s    r0   test_extremes_xzTestExponNorm.test_extremes_x  s    EO//a88#>>>EO//a88#>>>EO//d;;SAAAEO//d;;SAAAAAr2   zx, K, expected))r  r{   g6
N-)r   r{   g՜n+H?)r   r{   gi?)r  r{   gbJI-)r]   r   gI8?)r]   r  gQ3|-0?c                 f    t          t          j                            ||          |d           d S rQ  )r   r6   rC  rf   )rp   r\   rD  rU   s       r0   test_std_pdfzTestExponNorm.test_std_pdf  s1     	++Aq118%HHHHHHr2   zx, K, scale, expected)r   r{   r   gVAҤ?)r>  {Gzt?r   g'^>)r  r{   r^   r~   )r  r{   r   gbr ;)r   r_  r   gVMe?c                     t           j                            |||          }|dk    r
|dk    sJ d S t          ||d           d S )Nr  r~   r   r   )r6   rC  rn   r   rp   r\   rD  rc   rU   rw  s         r0   test_cdf_small_KzTestExponNorm.test_cdf_small_K  sU     O1E22s??888888Axe444444r2   )r]   r{   r   ghG}$;)rd   rO  r   g]fJ?)r   rO  ry   g31"g#;)r]   rO  ry   gf
+-)r  rO  ry   r~   )r  r_  r   ga9S?c                     t           j                            |||          }|dk    r
|dk    sJ d S t          ||d           d S )Nr  r~   -a=r   )r6   rC  r  r   rQ  s         r0   test_sf_small_KzTestExponNorm.test_sf_small_K  sU     Oq!511s??888888Axe444444r2   N)r   r   r   rB  r   r#  rL  r   r   r   rN  rR  rU  r8   r2   r0   r9  r9    s       9 9 96L L L
L L L
B B B$ [-B B BC CI IC CI [4>>>DDD444GGG???	AB B5 5B B5& [4BBB@@@DDDFFF333@@@BC C5 5C C5 5 5r2   r9  c                       e Zd Zd Zd Zej                            dg d          d             Zej                            dg d          d             Z	dS )	TestGenExponc                     ddl m} t          j                            t          j        ddd          ddd          }t           ||d          dd           d S )	Nr   )simpsr]   r{   ry   r}   )dxr   )scipy.integraterY  r6   genexponrf   rA  r  r   )rp   rY  rw  s      r0   test_pdf_unity_areaz TestGenExpon.test_pdf_unity_area  sd    ))))))Nu|Ar488#sCHHEE!---q!44444r2   c                     t           j                            t          j        ddd          ddd          }t          t          j        d|k    |dk    z                       d S )Nr   r]   r{   ry   r}   r   )r6   r\  rn   rA  r  r	   rB  )rp   rn   s     r0   test_cdf_boundszTestGenExpon.test_cdf_bounds  sV    n  aT!:!:CcJJ	18q12233333r2   zx, p, a, b, c))r>  gM <r   rd   r  )r   g%DYY?ry   rd   r   )r   gS4z?      #@rd   ry   )r{   ga^5?r  r   ry   )r  gs%)?r  r   ry   )r
  gdm?r   r   ry   c                     t           j                            ||||          }t          ||d           t           j                            ||||          }t          ||d           d S r  )r6   r\  r  r   r  )rp   r\   rw  r.   r/   r  r  r  s           r0   r  zTestGenExpon.test_sf_isf  sj     ^q!Q**AE****n  Aq!,,QU++++++r2   ))r   g;\i?ry   rd   r   )r   gu0?r`  rd   ry   )r{   g-%I?r  r   ry   )r  g]d?r  r   ry   )r
  g泩'?r   r   ry   c                     t           j                            ||||          }t          ||d           t           j                            ||||          }t          ||d           d S r  )r6   r\  rn   r   r  )rp   r\   rw  r.   r/   r  rn   r  s           r0   r  zTestGenExpon.test_cdf_ppf  sj     n  Aq!,,QU++++n  Aq!,,QU++++++r2   N)
r   r   r   r]  r_  r   r   r   r  r  r8   r2   r0   rW  rW    s        5 5 54 4 4  [_I I IJ J, ,J J, [_J J JK K, ,K K, , ,r2   rW  c                       e Zd Zd ZdS )TestTruncexponc                     ddg}ddg}ddg}t          t          j                            ||          |d           t          t          j                            ||          |d	           d S )
Nr  r^   g_93@gBX@g,M<gǃ@֫5r  r   r  )r   r6   
truncexponr  r  )rp   r/   r\   r  s       r0   r  zTestTruncexpon.test_sf_isf*  sx     I	"%'=>(++Aq113UCCCC(,,S!44aeDDDDDDr2   N)r   r   r   r  r8   r2   r0   rd  rd  (  s(        E E E E Er2   rd  c                       e Zd Zd ZdS )TestExponpowc                     t          t          j                            dd          d           t          t          j                            t          j                            dd          d          d           d S )Nr  r}   r}  r   r  )r   r6   exponpowrn   r  r  ru   s    r0   r  zTestExponpow.test_tail5  si    EN..ub995AAAEN..u~/@/@B/G/GLL	 	 	 	 	r2   N)r   r   r   r  r8   r2   r0   rh  rh  4  s#            r2   rh  c                        e Zd Zd Zd Zd ZdS )TestSkellamc                     t          j        dd          }d\  }}t          j        g d          }t          t          j                            |||          |d           d S )Nr  r>  r  )gYjP'?g$S?gQ`s2?gC/qF?gD<]Y?g/Xj?g86y?g]a¨?g:?g?gQ>?g?g:?g]a¨?g96?g0X?gA<]?gB/q?gQ`s?g$S?gYjP'?gX_?g+rx?gfSr?gJXx~?rX  )rA  r  r   r   r6   skellamrQ  )rp   rY   mu1mu2skpmfRs        r0   rl  zTestSkellam.test_pmf<  sm    Lb!!S- - -. . 	EM--ac::FBOOOOOOr2   c                     t          j        dd          }d\  }}t          j        g d          }t          t          j                            |||          |d           d S )Nr  r>  r  )gƃQ?gS`X'?gVy)>?g:	 S?gei.f?gȼJ]x?g)?g{^'+i?gLIg>?gnZ?g?rvͪ?gA?g0?g#J?gqSm
.?g~B?gd?gFBD?gQ9?gmF^?gcMy?gGJq?gC^c?g.){?gñݸ?r   rX  )rA  r  r   r   r6   rn  rn   )rp   rY   ro  rp  skcdfRs        r0   r]  zTestSkellam.test_cdfQ  sm    Lb!!S- - -. . 	EM--ac::FANNNNNNr2   c                     d\  }}}t          t          j                            |||          dd           t          t          j                            |||          dd           d S )N)r   r   gs1Cr   r  r   r   )r   r6   rn  rQ  rn   )rp   r\   ro  rp  s       r0   test_extreme_mu2zTestSkellam.test_extreme_mu2f  se    .3))!S#66FFFF))!S#66FFFFFFr2   N)r   r   r   rl  r]  ru  r8   r2   r0   rl  rl  ;  sL        P P P*O O O*G G G G Gr2   rl  c                      e Zd Zd Zd Z ej        d          d             Zej        	                    dddg          ej        	                    d	g d
          ej        	                    dg d          ej        	                    dd  e
dd          D                        ej        d          d                                                             ZdS )TestLognormc                     t          j                    5  t          j        dt                     t          j                            g dd          }t          |g d           d d d            d S # 1 swxY w Y   d S )Nrt  r   ry   r   r   )r~   g~r?g e3E?)rx  ry  rz  r{  r6   r&  rf   r   rp   rf   s     r0   rS  zTestLognorm.test_pdfn  s     $&& 	J 	J!'>:::-##KKK33C%c+H+H+HIII	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	Js   AA00A47A4c           	         d\  }}}t          t          j                            ||z
  |          t          j                            t          j        ||z
            |z                       t          t          j                            ||z
  |          t          j                            t          j        ||z
            |z                       d S )N)g(\5i@   gOn?rK   )r   r6   r&  r  r  rg   r  rw  )rp   r  r  sigmas       r0   rk  zTestLognorm.test_logcdfv  s    *B((B%(88
bfRUmmE&9::	< 	< 	<++BrEU+;;
((2u)<==	? 	? 	? 	? 	?r2   r  r  c                 @    t           j                            d          S r3  r	  ru   s    r0   r   zTestLognorm.rng~  r
  r2   r   rZ   rd   r   )r   r   rd   r   )r  r   r   r.  c                     g | ]}d |v |	S r0  r8   )r>   es     r0   r@   zTestLognorm.<listcomp>  r2  r2   )FTr   r3  r5  r6  c                     t           j                            d||||          }i }	|r||	d<   |r||	d<   |r||	d<   t          t           j        |fi |	 d S )Nr^   )r   rL   rc   rb   r   r   r   r   )r6   r&  r   r   r9  s
             r0   r   z'TestLognorm.test_fit_MLE_comp_optimizer  s     }  cYi%,3 ! @ @  	#"DJ 	#"DL 	'&DN%emTBBTBBBBBr2   N)r   r   r   rS  rk  r   r  r   r   r   r%   rg   rD  r   r8   r2   r0   rw  rw  m  sA       J J J? ? ? V^*%%%+ + &%+ [[2q'22[Y


33[[***55[<- -q)I)I)I - - -. . R["""C C #". . 65 43 32C C Cr2   rw  c                   Z   e Zd Zd Zd Zd Zd Zej        	                    e
d          d             Zej        	                    e
d          d             Zej        	                    e
d          d	             Zd
 Zej                            ed          d             Zej                            dej        j        ej        j        g          ej                            dddg          d                         Zej                            dg d          d             ZdS )TestBetac                     t           j                            ddd          }t          |d           t           j                            ddd          }t          |t          j                   d S )Nr   r   ry   g;B.)r6   r  r   r   rg   r  rp   r   s     r0   r\  zTestBeta.test_logpdf  s\    ""1a--FN333""1c1--FBF+++++r2   c                 `   d\  }}t          j        g d          }t          j        ||          }t	          |                    |                                          d           t	          |                    |          t          j        |                    |                               d S )Ni  i  r  ry   r  gƒ)	rg   r   r6   r  r   r   rn  rf   r   rp   r  r  r\   r/   s        r0   test_logpdf_ticket_1866z TestBeta.test_logpdf_ticket_1866  s    tH___%%Jud##))+=>>>a"&!"5"566666r2   c                 `    g d}t          t          t          j        j        |ddd           d S )NrZ   ry   r  r   r   r*  )r   r   r+  )r?  r  r6   r  r   r  s     r0   test_fit_bad_keyword_argsz"TestBeta.test_fit_bad_keyword_args  s=    OOi1$	& 	& 	& 	& 	& 	&r2   c                 ^    g d}t          t          t          j        j        |dd           d S )Nr  ry   )fafix_a)r?  r  r6   r  r   r  s     r0   #test_fit_duplicated_fixed_parameterz,TestBeta.test_fit_duplicated_fixed_parameter  s0     OOj%*.!3GGGGGGr2   zOverflow, see gh-14901reasonc                 p    d\  }}}t          t          j                            |||          d           d S )N)g?g     R@g   0xAgx)>)r   r6   r  r  )rp   rw  r.   r/   s       r0   test_issue_12635zTestBeta.test_issue_12635  s8     71a
q!Q//1FGGGGGr2   c                 >   t          j        g d          }t          j        g d          }d}t          j                            ||dz   d|z
            }t          ||           t          j                            ||dz   d|z
            }t          ||           d S )N)g@3@?g^?gNC?)r]   r^   r   r1  r   r   )rg   r   r6   r  r  r   r  )rp   inv_R
count_listrw  invr   s         r0   test_issue_12794zTestBeta.test_issue_12794  s      1 1 1 2 2 Xooo..
jnnQ
Q0CDDU###jmmCa*1DEEQr2   c                     d}t          j        dd          }d}d|z
  |dz   ||z
  }}}t          j                            |||          }t          j                            |||          }t          |d|z
             d S )Nh㈵>r   r  r   )rg   r  r6   r  r  rn   r   )	rp   alpha_2count_nobsr  r.   r/   r  r   s	            r0   test_issue_12796zTestBeta.test_issue_12796  s     1b!!g+vz4&=a1jnnQ1%%jnnS!Q''Q[)))))r2   c                    d\  }}t          t          j                            d||          t          j                   d\  }}t          t          j                            d||          t          j                   d\  }}t          t          j                            d||          d           t          t          j                            d||          d           d\  }}t          t          j                            d||          d           t          t          j                            d	||          d           d S )
NrU  r   )r  r   r   )r   r   r   +ph  )r   r   rU  )r   r6   r  rf   rg   r  )rp   r.   r/   s      r0   r  zTestBeta.test_endpoints  s    1UZ^^Aq!,,bf555 1UZ^^Aq!,,bf555 1UZ^^Aq!,,a000UZ^^FAq111555 1UZ^^Aq!,,a000UZ^^Ha33Q77777r2   zDoes not convert boost warningc                     d\  }}}t          j        t                    5  t          j                            |||           d d d            d S # 1 swxY w Y   d S )N)gףp=
?g   vH7B  @0B)r   warnsr{  r6   r  r  )rp   r  r.   r/   s       r0   test_boost_eval_issue_14606z$TestBeta.test_boost_eval_issue_14606  s    '1a\.)) 	$ 	$JNN1a###	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$s   "AAAr  a, b)r        )@)r  r  c                 H    d}	  ||||           d S # t           $ r Y d S w xY w)Nr  )OverflowError)rp   r  r.   r/   rw  s        r0    test_beta_ppf_with_subnormal_a_bz)TestBeta.test_beta_ppf_with_subnormal_a_b  sG    
 
	F1aOOOOO 	 	 	 DD	s    
!!r  ))ry   ry   gο)r_  r   g )r   r  g&׾k )r   r   g*)Mc                 p    t          t          j        ||                                          |           d S rs   )r   r6   r  rE   r  s       r0   rr  zTestBeta.test_entropy  s2     	
1a((0022C88888r2   N)r   r   r   r\  r  r  r  r   r   skipifMACOS_INTELr  r  r  r  xfailr   r  r   r6   r  r  r  r  rr  r8   r2   r0   r  r    s       , , ,7 7 7& & &
H H H [,DEE	H 	H FE	H [,DEE    FE " [,DEE	* 	* FE	*8 8 8. [w'GHH$ $ IH$
 [X

'GHH[Vnn%EFF  GF IH@ [[D D DE E
9 9E E
9 9 9r2   r  c                   f   e Zd Zg dZd Zd Zej                            dg d          d             Z	ej                            de          d             Z
ej                            d	eg d
z             d             Zej                            d	ddg          d             Zd Zd Zd ZdS )TestBetaPrime))rC  r   r   D>?)r  r   r   m嗽?)r   r   rZ   gPK?)r   r   r   g%p?)r  r   rZ   g#|/?)r  r  r  gsM
<)r  r   r   $5Є*?)^ 9^;r   rZ   gompP?)r  r  r  g7j"!9)r  r   r   z^J?)r  r   rZ   gܷ"+>)r  r  r  grNs: )r  r   r   gK>c                    d\  }}t          j        g d          }t          j        ||          }t	          t          j        |                    |                                                               t          |	                    |          t          j
        |                    |                               d S )Nr  r  )rg   r   r6   r  r	   r  r   rB  r   rf   r   r  s        r0   r\  zTestBetaPrime.test_logpdfB  s    tH___%%OE4((AHHQKK((,,..///a"&!"5"566666r2   c                    t           j                            ddd          }t          |d           d\  t	          j        g d          }t           j                            |          }t          t	          j        |                                                     t           j	        j
        fd|D             }t          ||dd	           d S )
Nr   r  r  r~   r  r  c                 @    g | ]} t           j        |          S r8   )r6   r  )r>   rJ  r  r  gen_cdfs     r0   r@   z*TestBetaPrime.test_cdf.<locals>.<listcomp>V  s+    JJJ''%/3t<<JJJr2   -=r   )r6   r  rn   r   rg   r   r	   r  rB  rC   _cdf_singler   )rp   r\   r!  cdfs_gr  r  r  s       @@@r0   r]  zTestBetaPrime.test_cdfI  s     O3,,QtH___%%""1eT22D!!%%''((( %1JJJJJJJJJf15999999r2   zp, a, b, expected))r{         ?r  gV)?)r  r  r  gWJB9*=)r  r  r  gOG J<)r;  r         @gΣ01)      ?r   r  g8ǘ`?)>q?r   rZ   gMDc                 l    t           j                            |||          }t          ||d           d S r  )r6   r  r  r   )rp   rw  r.   r/   rU   r\   s         r0   r`  zTestBetaPrime.test_ppfh  s8     O1a((8%000000r2   z
x, a, b, pc                 h    t          t          j                            |||          |d           d S r  )r   r6   r  r  )rp   r\   r.   r/   rw  s        r0   test_ppf_gh_17631zTestBetaPrime.test_ppf_gh_17631u  s1    ++Aq!44aeDDDDDDr2   zx, a, b, expected))r  r  r  rR  )r  r   rZ   gV[?)rC  r   rZ   r  c                 h    t          t          j                            |||          |d           d S r  )r   r6   r  rn   )rp   r\   r.   r/   rU   s        r0   test_cdf_gh_17631zTestBetaPrime.test_cdf_gh_17631y  s3     	++Aq!44hUKKKKKKr2   )r  r   rZ   g%?)r  r   r   goXr?c                 |    t           j                            |||          }|dk     sJ t          ||d           d S )NrU  gh㈵>r   )r6   r  rn   r   )rp   r\   r.   r/   rU   r  s         r0   test_cdf_extreme_tailsz$TestBetaPrime.test_cdf_extreme_tails  sE     O1a((3wwww8$//////r2   c                     g d}g d}g d}g d}t           j                            |||          }t          ||d           d S )N)r   r   rd   r   r   r   r   r   r   r   r   r   r  r  )r   rd   r   rZ   rZ   rZ   rZ   r   r   r   r   r   r  r  )r  rI  ꌠ9Y>)FrC  r  r  r  rC  r  r  r  r  r  r  )g/:g  U/7gKH9g<![a?gw 4?g)J?g5?r  r  r  r  g%?gsM
<rR  r  r   )r6   r  r  r   )rp   r.   r/   r\   r  	sf_valuess         r0   r  zTestBetaPrime.test_sf  s|        0 0 0; ; ;
 O&&q!Q//		3U333333r2   c                     t           j                            g ddd           t          j        dd                               d           d S )N)rZ   r   r  r  皙?r   r   r>  r@  rW  )r6   r  r   ru   s    r0   test_fit_stats_gh18274z$TestBetaPrime.test_fit_stats_gh18274  sQ     	666QqIII!q!!!''/////r2   c                     t           j        dg}t          j        dddg                              d          }t          ||           d S )NgooB?rd   r  gffffff@r   )rg   r  r6   r  r  r   )rp   r  r   s      r0   test_moment_gh18634z!TestBetaPrime.test_moment_gh18634  sJ     v()oa#s,,33A66S!!!!!r2   N)r   r   r   cdf_valsr\  r]  r   r   r   r`  r  r  r  r  r  r  r8   r2   r0   r  r  %  sq         H 7 7 7: : :> [	B 	B 	B 1 1 1 [\844E E 54E [ 
 
 
 	
 L L L [	.	/	12 20 0	2 204 4 4*0 0 0	" 	" 	" 	" 	"r2   r  c                       e Zd Zd Zd Zd Zd Zej        	                    dddg          d             Z
ej        	                    d	g d
          d             ZdS )	TestGammac                     t           j                            ddd          }t          |d           t           j                            ddd          }t          |d           d S )	NZ   i  r  r  g
CTb?r   r]   gBΖ?)r6   rZ  rf   r   rz  s     r0   rS  zTestGamma.test_pdf  sZ    koob#To22C---kooa4o00C+++++r2   c                 f    t           j                            dd          }t          |d           d S r  )r6   rZ  r   r   r  s     r0   r\  zTestGamma.test_logpdf  s1     ##Aq))FA&&&&&r2   c                 ^    g d}t          t          t          j        j        |dd           d S )Nr  r   r*  )r   r+  )r?  r  r6   rZ  r   r  s     r0   r  z#TestGamma.test_fit_bad_keyword_args  s.    OOi!!8LLLLLLr2   c                     t          j        t          j                            dd          dd          sJ t          j        t          j                            dd          dd	          sJ d S )
Nr;  r   gplC@r~  r   rO  r^   g1}t@r   )rg   iscloser6   rZ  r  ru   s    r0   r  zTestGamma.test_isf  s    " z%+//%33+%9 9 9 	9 	9 	9z%+//%55+%9 9 9 	9 	9 	9 	9 	9r2   rc   rU  rV  c                 |    t           j                            |dz  |dz  d|          }t          |dd           d S )N   r  r   r  g>S*r   r   )r6   rZ  r/  r   rp   rc   r  s      r0   r0  zTestGamma.test_delta_cdf  sF     &&uSy%)Qe&LL6UCCCCCCr2   za, ref, rtol))r  gt.r   )rd   r]  r   )r^   gX>k-־@r   )r  gwM7@r   )g NgmCg%og$6@r   )r  oܘ#]@r   c                 d    t          t          j                            |          ||           d S rL  )r   r6   rZ  rE   )rp   r.   r  r   s       r0   rr  zTestGamma.test_entropy  s/     	++A..$??????r2   N)r   r   r   rS  r\  r  r  r   r   r   r0  rr  r8   r2   r0   r  r    s        , , ,' ' 'M M M9 9 9, [WsCj11D D 21D [^B B BC C@ @C C@ @ @r2   r  c                       e Zd Zd Zej                            dg d          d             Zej                            dg d          d             Zej                            dg d          d	             Z	d
 Z
dS )
TestDgammac                    t           j                            d          }d}|                    d|          }|                    d|          }t
          j                            ||          }t
          j                            t          j	        |          |          dz  }t          ||           t          j        |          }t          |                    |          |           d S )Nl   OP($ r]   r  )r  r   rd   )rg   r   r   normalrT  r6   dgammarf   rZ  r   r   r   )rp   r   r   r\   r.   r   r  r?   s           r0   rS  zTestDgamma.test_pdf   s    i##$788JJRdJ++KKRdK++lq!$$koobfQii++a/S!!!|ATXXa[[#&&&&&r2   zx, a, expected))r  r   ggrU>)r-  r   g$IC<)ir   g2Wj<)r
  g~)A.=)r   r   gf?c                    t           j                            ||          }t          ||d           t           j                            ||          }t          ||d           t           j                            | |          }t          ||d           t           j                            ||          }t          || d           d S r_  )r6   r  rn   r   r  r  r  )rp   r\   r.   rU   rn   r  r  r  s           r0   test_cdf_ppf_sf_isf_tailz#TestDgamma.test_cdf_ppf_sf_isf_tail  s     lq!$$XE2222lx++QU++++\__aR##H51111lx++aRe,,,,,,r2   r`  ))r  gmqn @)?g?)rW  gx?c                 d    t          t          j                            |          |d           d S r  r   r6   r  rE   rb  s      r0   rr  zTestDgamma.test_entropy%  s/      	,,Q//5AAAAAAr2   ))r  r  )r  g>_)r  g5i)r  go@)  4&kCg4Fa3@)r  grO]@c                 d    t          t          j                            |          |d           d S r  r  rb  s      r0   test_entropy_entreme_valuesz&TestDgamma.test_entropy_entreme_values7  s/    " 	,,Q//5AAAAAAr2   c                    t          j        g d          }t          j                            |          }t          t          |                    D ]3}||         t          j                            ||                   k    sJ 4d S )N)r   r   rI  r  )rg   r   r6   r  rE   r   r  )rp   r\   r  r  s       r0   test_entropy_array_inputz#TestDgamma.test_entropy_array_inputJ  s~    H'''((L  ##s1vv 	6 	6AQ45<//!5555555	6 	6r2   N)r   r   r   rS  r   r   r   r  rr  r  r  r8   r2   r0   r  r    s        
' 
' 
'* [-: : :; ;- -; ;- [X8 8 89 9B B	9 9B [X: : :; ;
B 
B; ;
B6 6 6 6 6r2   r  c                   f    e Zd Zd Zd Zej                            dg d          d             ZdS )TestChi2c                     t          t          j                            dd          dd           t          t          j                            dd          dd           d S )Nr   gޞw1D?r  rX  r^   g6:֜?r   r6   chi2rf   ru   s    r0   rw  zTestChi2.test_precisionS  sj    EJNN4668N$&	( 	( 	( 	(EJNN3446J$&	( 	( 	( 	( 	( 	(r2   c                    d}t           j                            d|          }t          |dd           t           j                            d|          }t          |dd           d}t           j                            d	|          }t          |d
d           t           j                            d|          }t          |dd           d S )Nr  gλm:=6g'bd5 <r  r   ry   gQ8@   gܐ؆0guu[9=rZ   g8-*@)r6   r  r  r   )rp   r  r\   s      r0   r`  zTestChi2.test_ppfY  s    JNN5"%%<5IIIIJNN3##7eDDDDJNN5"%%:GGGGJNN3##8uEEEEEEr2   r  ))r  gܫ>)r   gƯʉ?)r^   gn>@)   g͔v0@)r  g9:3@c                 r    t          t          j        |                                          |d           d S r   )r   r6   r  rE   r  s      r0   rr  zTestChi2.test_entropyq  s3     	
2..00#EBBBBBBr2   N)	r   r   r   rw  r`  r   r   r   rr  r8   r2   r0   r  r  Q  s{        ( ( (F F F0 [Y: : :; ;C C; ;C C Cr2   r  c                   l    e Zd Zd Zd Zd Zej                            dddg          d             Z	dS )	TestGumbelLc                     t          j        dd          }t          j                            |          }t          j                            |          }t          ||           d S Nr6  r  )rg   rZ  r6   r  rn   r  r   r  s       r0   r  zTestGumbelL.test_cdf_ppf}  sS    Kb!!Nq!!^""2r2   c                    t          j        dd          }t          j                            |          }t          j                            |          }t          j        |          }t          j        |           }t          ||           d S r  )
rg   rZ  r6   r  r  rw  r   r   expm1r   )rp   r\   r  r  urA  s         r0   ry  zTestGumbelL.test_logcdf_logsf  sr    Kb!!N!!!$$N  ##F1II]11r2   c                     t          j        dd          }t          j                            |          }t          j                            |          }t          ||           d S )Nr  r   )rg   rZ  r6   r  r  r  r   r  s       r0   r  zTestGumbelL.test_sf_isf  sS    KQNa  ^""2r2   rb   r   r   c                     t           j                            d|          }t           j                            ||          \  }}t	          ||           d S )Nr^   )r   rb   r   )r6   r  r   r   r   )rp   rb   r   
fitted_locr   s        r0   test_fit_fixed_paramz TestGumbelL.test_fit_fixed_param  sR     ~!!s!44**4c*::
AZ%%%%%r2   N)
r   r   r   r  ry  r  r   r   r   r  r8   r2   r0   r  r  {  ss               [URG,,& & -,& & &r2   r  c                       e Zd Zd Zd ZdS )TestGumbelRc                 d    t          t          j                            d          dd           d S )Nr<  ?~T}%m;r~  r   )r   r6   r  r  ru   s    r0   r  zTestGumbelR.test_sf  s=     	))"--/E"	$ 	$ 	$ 	$ 	$ 	$r2   c                 d    t          t          j                            d          dd           d S )Nr;  r  r~  r   )r   r6   r  r  ru   s    r0   r  zTestGumbelR.test_isf  s=     	**5113D"	$ 	$ 	$ 	$ 	$ 	$r2   N)r   r   r   r  r  r8   r2   r0   r  r    s2        $ $ $$ $ $ $ $r2   r  c                      e Zd Zej        d             Zej        d             Zej        d             Zej        	                    d ej
        d           ej
        dej        j                  g          ej        	                    dd	d
g          ej        	                    dg d          ej        	                    dddg          d                                                 Zej        j        ej        	                    dddg          d                         Zd Zej                            d          ej        	                    dddg          ej        	                    dd	d
g          d                                     Zd Zd Zd Zej        	                    d  ej
        g d!g d"g d#           ej
        g d$g d%g d&ej        j                   ej
        g d' ej        d(d)d*           ej        d+dd,          ej        j                  g          d-             Zej        	                    d  ej
        g d!g d"g d#           ej
        g d$g d%g d&ej        j                   ej
        g d' ej        d(d)d*           ej        d+dd,          ej        j                  g          d.             Zej        	                    d/d0dg          ej        	                    d1d2d3g          d4                         Zej        	                    d5d6d7gd8d7gg          d9             Zej        	                    d:d;d0ej        ej        ej        fgd<d=gg          d>             Zej        	                    d?g d@          ej        	                    dAej        j         dB ej        dCd0dD          dEfej        j!        dB ej        dCd0dD          dEfej        j         dF ej        d0dGdD          dBfej        j!        dF ej        d0dGdD          dEfg          dH                         Z"dIS )JTestLevyStablec                     t          j        t          t                    j        dz            }t           j        j                            |j        d          }|S )a  Sample data points for pdf computed with Nolan's stablec

        See - http://fs2.american.edu/jpnolan/www/stable/stable.html

        There's a known limitation of Nolan's executable for alpha < 0.2.

        The data table loaded below is generated from Nolan's stablec
        with the following parameter space:

            alpha = 0.1, 0.2, ..., 2.0
            beta = -1.0, -0.9, ..., 1.0
            p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5,
        and the equivalent for the right tail

        Typically inputs for stablec:

            stablec.exe <<
            1 # pdf
            1 # Nolan S equivalent to S0 in scipy
            .25,2,.25 # alpha
            -1,-1,0 # beta
            -10,10,1 # x
            1,0 # gamma, delta
            2 # output file
        z.data/levy_stable/stable-Z1-pdf-sample-data.npyx,p,alpha,beta,pctnames	rg   loadr   __file__parentcorerecords
fromarraysTr  s     r0   nolan_pdf_sample_dataz$TestLevyStable.nolan_pdf_sample_data  sO    6 wNN!<=
 
 w))$&8L)MMr2   c                     t          j        t          t                    j        dz            }t           j        j                            |j        d          }|S )a#  Sample data points for cdf computed with Nolan's stablec

        See - http://fs2.american.edu/jpnolan/www/stable/stable.html

        There's a known limitation of Nolan's executable for alpha < 0.2.

        The data table loaded below is generated from Nolan's stablec
        with the following parameter space:

            alpha = 0.1, 0.2, ..., 2.0
            beta = -1.0, -0.9, ..., 1.0
            p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5,

        and the equivalent for the right tail

        Ideally, Nolan's output for CDF values should match the percentile
        from where they have been sampled from. Even more so as we extract
        percentile x positions from stablec too. However, we note at places
        Nolan's stablec will produce absolute errors in order of 1e-5. We
        compare against his calculations here. In future, once we less
        reliant on Nolan's paper we might switch to comparing directly at
        percentiles (those x values being produced from some alternative
        means).

        Typically inputs for stablec:

            stablec.exe <<
            2 # cdf
            1 # Nolan S equivalent to S0 in scipy
            .25,2,.25 # alpha
            -1,-1,0 # beta
            -10,10,1 # x
            1,0 # gamma, delta
            2 # output file
        z.data/levy_stable/stable-Z1-cdf-sample-data.npyr  r  r  r  s     r0   nolan_cdf_sample_dataz$TestLevyStable.nolan_cdf_sample_data  sP    J wNN!<=
 
 w))$&8L)MMr2   c                 b    t          j        t          t                    j        dz            }|S )a&  Sample data where loc, scale are different from 0, 1

        Data extracted in similar way to pdf/cdf above using
        Nolan's stablec but set to an arbitrary location scale of
        (2, 3) for various important parameters alpha, beta and for
        parameterisations S0 and S1.
        z1data/levy_stable/stable-loc-scale-sample-data.npy)rg   r  r   r  r  r  s     r0   nolan_loc_scale_sample_dataz*TestLevyStable.nolan_loc_scale_sample_data  s1     wNN!?@
 
 r2   sample_sizer<  r  marksparameterizationS0S1z
alpha,beta))rU  r   )rU  r   )r  r   )r  ry   zgamma,deltar   r   r  c                     |t           j        _        t          j        ||||          }t          j        |                    |d          |j                  \  }}	|	dk    sJ d S )N)r  r  rc   rb   r4  r  r   )r6   levy_stabler  r  r   rn   )
rp   r  r  r  rZ  r  r  lsr   rw  s
             r0   rK  zTestLevyStable.test_rvs  sp    & .>*d%U
 
 
 |FF$F77
 
1 4xxxxxxr2   r  ry   r   c                     t           j                            d           d}d}d}t          j                            ||||d          }t          j        |d||||f          \  }}|d	k    sJ d
S )z3Additional test cases for rvs for alpha equal to 1.h:rU  ry   r  r  rb   rc   r   r$  r  r{   N)rg   r   r   r6   r$  r   r  )rp   r  r  rb   rc   r\   statrw  s           r0   test_rvs_alpha1zTestLevyStable.test_rvs_alpha1)  s     		y!!!!!%3e'+ " - -,q-%*D#u$=? ? ?a4xxxxxxr2   c                    g d}t           j                            |          \  }}}}t          |ddd           t	          |dd           t	          |dd	           t	          |d
d           |g dz   }t           j                            |          \  }}}	}
t          |d           t          |d           t	          |
dd	           t	          |	dd	           d S )N)wgr,  r~   r~   r~   r~   羼 u?r-  r-  r-  r-  67',?r.  r.  r.  r.  tA}˜.?r/  r/  r/  r/  Gz?r   r{   rh  )\(̿rd   gۧ1?r   g9]c?)r/  r/  r/  r/  r/  r   gv?r.  )r6   r$  r  r   r   r   rp   r\   alpha1beta1loc1scale1r  alpha2beta2r  r  s              r0   r  zTestLevyStable.test_fit7  s   
 
 

 ',&7&A&A!&D&D#tV148888E4+++FGQ///'1	
 	
 	

 9999&+&7&A&A"&E&E#tVVQUBFFA...D&!,,,,,r2   zUnknown problem with fitstart.r  zalpha,beta,delta,gamma)r  r  rd   r   )rU  r  rd   r   parametrizationc                     |t           j        _        t           j                            ||||dd          }t           j                            |          }|\  }}	}
}t          ||||g||	|
|gd           dS )z7Test that fit agrees with rvs for each parametrization.r  r4  rb   rc   r   r   r{   r   N)r6   r$  r9  r   r  r   )rp   r  r  r  rZ  r9  r   r   	alpha_obsbeta_obs	delta_obs	gamma_obss               r0   test_fit_rvszTestLevyStable.test_fit_rvsO  s     -<) $$4U%e$ % 
 
 ))$//471	8Y	D%')Y7	
 	
 	
 	
 	
 	
r2   c                 x   t          j        g d          }t          j                            |          \  }}}}t          j                            |           \  }}}}	t          |d           |dk    sJ t          ||           t          ||            t          ||            t          |	|           d S )Nr   r   r   r   r]   r]   r]   r9  r9  r^   r^   r   r   )rg   r   r6   r$  r  r   r   )
rp   r\   r3  r4  r5  r6  r7  r8  r  r  s
             r0   test_fit_beta_flipz!TestLevyStable.test_fit_beta_fliph  s    H???@@&+&7&A&A!&D&D#tV&+&7&A&A1"&E&E#tVUAqyyyyFF+++EE6***D4%(((FF+++++r2   c                 V   d}t          j        g d          }t          j                            |           \  }}}}t          j                            | |z             \  }}}	}
t          ||           t          ||           t          |	||z              t          |
|           d S )Nr   rB  )rg   r   r6   r$  r  r   )rp   SHIFTr\   r3  r4  r5  r6  r7  r8  r  r  s              r0   test_fit_delta_shiftz#TestLevyStable.test_fit_delta_shiftt  s    H???@@&+&7&A&A1"&E&E#tV&+&7&A&A1"u*&M&M#tVFF+++E5)))D$,///FF+++++r2   c                    g d}t           j                            |          \  }}}}|dk     sJ d|             |t          |          k     sJ dt          |           d|             g d}t           j                            |          \  }}}	}
|dk    sJ d|             |	t	          |          k    sJ dt	          |           d|	             d S )	N)r   r   r   r   r]   r]   r]   r9  r9     rH  r   zExpected alpha < 1, got zExpected loc < z, got )r   r   r   r   r]   r]   r]   r9  r9     rI  zExpected alpha > 1, got zExpected loc > )r6   r$  r  r  rj  r2  s              r0   test_fit_loc_extrapz"TestLevyStable.test_fit_loc_extrap  s    666&+&7&A&A!&D&D#tVzzz>f>>zzzc!ff}}}DADDdDD}}}777&+&7&A&A"&E&E#tVzzz>f>>zzzc"gg~~~FRFFFF~~~~~r2   z pct_range,alpha_range,beta_range)r{   ry   r%  )rZ   r   rd   )r   r   r  )r{   r   ry   r  r%  )rZ   ry   r   r  rd   )r   r   r   r  r  r   )r{   r   rZ   r   ffffff?ry   ?rc  r  r  r%  rZ   rd   r  r      c                 p   |}t          j                    }|j        dk    o
|j        dk    d                    |j        |j        |j        g          }ddfdgddfd	gddfd
gddfdgddfdgddfdgg}t          |          D ]\  }	\  }
}}|
t          j        _	        || ||                   n|}t                      5 }|                    t          d           t          j                            |d         |d         |d         dd          }t          j        d          5  t!          |g d|t          j        ||d         z
            t          j        ||d         z
            t          j        |d                   z  g          }ddd           n# 1 swxY w Y   ||d         |k    t          j        |          z           }t'          ||d         |d|	d |
d!|d"|j        j        d#|
d$%           ddd           n# 1 swxY w Y   dS )&z2Test pdf values against Nolan's stablec.exe outputLinuxi686/dnir  c           	      r   t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    | d         dk    z  | d         dk    | d         dk    z  | d         dk    z  z  | d         dk    t          j        | d         d	d
g          z  z  | d         dk    t          j        | d         ddg          z  z  | d         dk    t          j        | d         ddg          z  z  | d         dk    t          j        | d         ddg          z  t          j        t          j        | d                   g d          z  z  | d         dk    t          j        | d         dg          z  t          j        t          j        | d                   dg          z  z  | d         dk    t          j        | d         ddg          z  t          j        t          j        | d                   g d          z  z  | d         dk    | d         dk    z  | d         dk    z  z  | d         dk    | d         dk    z  | d         dk    z  z  | d         dk    | d         dk    z  | d         dk    z  z  | d         dk    t          j        | d         dg          z  t          j        t          j        | d                   g d          z  z  | d         dk    t          j        | d         ddg          z  t          j        t          j        | d                   g d          z  z  | d         dk    t          j        | d         d	d
g          z  t          j        t          j        | d                   ddg          z  z  | d         dk    z   z  S )Npctr  r  r   ry   r  r  r  r{   r%  r  r   r  r  rZ   r   rc  )ry   r  r  rK  rL  )gٿ333333ӿr  r  ry   rU  rU  rZ   r  r  r  )r  r  rU  r  rW  )rg   isinr   r  alpha_range
beta_range	pct_ranges    r0   rM   z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>  s   GAeHi00GAgJ445GAfIz223
 vY!^uX_. vY#-wZ3.0uX_. wZ3.GAeHsCj99: wZ3.GAeHsCj99:$ wZ3.GAeHr2h778%, wZ3.GAeHsCj99:GBF1V9$5$5|||DDE-6 wZ3.GAeHrd334GBF1V9$5$5t<<=7@ wZ3.GAeHsCj99:GBF1V9$5$57M7M7MNNOA#J wZ3.vY#-/uX-/K(T wZ3.vY$.0uX-/U-^ wZ3.vY#-/uX-/_2h wZ2-GAeHrd334GBF1V9$5$57G7G7GHHIi7r wZ2-GAeHsCj99:GBF1V9$5$5|||DDEs<| wZ2-GAeHsCj99:GBF1V9$5$5RyAAB}AF 7s*GC,EH r2   	piecewiser1  c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  | d         dk    z  S )NrT  r  r  r  rU  rg   rW  rX  s    r0   rM   z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>  sq    GAeHi00GAgJ445GAfIz223 wZ#%' wZ2%	' r2   c                     | d         dk     z  t          j        | d                   z  dv z  t          j        | d                   z  S )Nr  rU  rT  r  r^  )r  rY  rZ  is_linux_32r[  s    r0   rM   z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>  s_    wZ2%$_&GAeHi001 ;&( GAfIz22	3 r2   g&.=c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  S )NrT  r  r  r  r^  rX  s    r0   rM   z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>  s^    GAeHi00GAgJ445GAfIz223 wZ3&( r2   fft-simpsonr  c                     | d         dk    t          j        | d                   z  t          j        | d                   z  t          j        | d                   z  S )Nr  r  rT  r  r^  rX  s    r0   rM   z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>  s^    wZ3&GAeHi001GAgJ445 GAfIz223 r2   r  c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  | d         dk     z  S )NrT  r  r  r   r  r^  rX  s    r0   rM   z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>'  sp    GAeHi00GAgJ445GAfIz223 wZ!^% wZ#%	' r2   Nz2Density calculations experimental for FFT method.*r\   r  r  r   r   rc   rb   r5  r>  calcabserrrelerrrw  ri  z	pdf test  failed with method 'z' [platform: z]

Ferr_msgverbose)platformunamesystemmachinejoin	processorr  r6   r$  pdf_default_methodr   recordr{  rf   rg   rD  r   r   isnanr   r   r  )rp   r  r[  rY  rZ  r   rp  platform_desctestsixdefault_methodr   filter_funcsubdatasuprw  subdata2failuresr`  s     ```             @r0   test_pdf_nolan_samplesz%TestLevyStable.test_pdf_nolan_samples  s   2 %   lg-I%-62I\5=%/:< < t J J J J J JL^ U % % % % % % U % % % % % % % W ' ' ' ' ' ' t & & & & & & t & & & & & &kC
L "+5!1!1)	 )	 B 3AE0 + 7 ;;t,,  =A "$$ $

"H   %))CLG$FO *   [h/// 	 	0444F1ws|#344F1ws|#344rvgcl7K7KK   H	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 $H%-(1++  CLD RR8L8L8L " "	 	 	 	7$ $ $ $ $ $ $ $ $ $ $ $ $ $ $)	 )	s9   A'H)A(F8,H)8F<<H)?F< AH))H-	0H-	c                    |}ddfdgddfdgddfdgdd	fd
gddfdgddfdgg}t          |          D ]\  }\  }}	}
|t          j        _        |
| |
|                   n|}t	                      5 }|                    t          d           t          j                            |d         |d         |d         dd          }t          j	        d          5  t          |g d|t          j        ||d         z
            t          j        ||d         z
            t          j        |d                   z  g          }ddd           n# 1 swxY w Y   ||d         |	k    t          j        |          z           }t          ||d         |	d|d|d|j        j        d|d !           ddd           n# 1 swxY w Y   dS )"z4 Test cdf values against Nolan's stablec.exe output.r\  r  c                    t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    t          j        | d         g d          z  | d         dk    z  | d         dk    t          j        | d         g d          z  | d         dk    z  z   z  S 	NrT  r  r  rU  )rU  r  r  r{   rZ   r  r  r%  r^  rX  s    r0   rM   z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>~  s    GAeHi00GAgJ445GAfIz223
 wZ2-GAfI/A/A/ABBCuX-/
 wZ2-GAfI??@uX-/	 r2   r   c                    t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    t          j        | d         g d          z  | d         dk    z  z  | d         dk    t          j        | d         g d          z  | d         dk    z  z  S r  r^  rX  s    r0   rM   z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>  s    GAeHi00GAgJ445GAfIz223 7r)&	+=+=+=>>?5T)+	 7r)&	???;;<5T)+ r2   rb  r  c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  S )NrT  r  r  333333?r^  rX  s    r0   rM   z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>  s^    GAeHi00GAgJ445GAfIz223 wZ#%' r2   r  c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  | d         dk    z  S )NrT  r  r  r  r  r^  rX  s    r0   rM   z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>  q    GAeHi00GAgJ445GAfIz223 wZ#%' wZ3&	( r2   r_  c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  | d         dk    z  S )NrT  r  r  r  r  r^  rX  s    r0   rM   z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>  r  r2   r{   c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  | d         dk    z  S )NrT  r  r  rU  r  r^  rX  s    r0   rM   z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>  r  r2   Nz[Cumulative density calculations experimental for FFT method. Use piecewise method instead.*r\   r  r  r   r   re  r5  r>  rf  rw  ri  z	cdf test rj  z'
rk  Frl  )r  r6   r$  cdf_default_methodr   rv  r{  rn   rg   rD  r   r   rw  r   r   r  )rp   r  r[  rY  rZ  r   ry  rz  r{  r   r|  r}  r~  rw  r  r  s     ```           r0   test_cdf_nolan_samplesz%TestLevyStable.test_cdf_nolan_samplesa  sw   2 % U % % % % % %, T $ $ $ $ $ $& t & & & & & & t & & & & & & t & & & & & & t & & & & & &GL
\ "+5!1!1'	 '	 B 3AE0 + 7 ;;t,,  =A "$$ "

"@  
 %))CLG$FO *   [h/// 	 	0444F1ws|#344F1ws|#344rvgcl7K7KK   H	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 $H%-(1++  CLDRR)=)=)=xxI!   7" " " " " " " " " " " " " " "'	 '	s9   A'G2A(E&G&E**G-E*.AGG	G	r  r   r9  rf   rn   c                    t          j                    }|j        dk    odt          j                    d         v }|r|dk    rt	          j        d           |}dt          j        _        dt          j        _	        ||d         |k             }d| t          j        _
        |d	v sJ |dk    rt          j        j        nt          j        j        } ||d
         |d         |d         dd          }	t          |	||         d           dS )zGTests for pdf and cdf where loc, scale are different from 0, 1
        rO  32bitr   rf   z4Test unstable on some platforms; see gh-17839, 17859r\  r  S)rf   rn   r\   r  r  rd   r   re  r  N)ro  rp  rq  architecturer   r   r6   r$  r  ru  r  rf   rn   r   )
rp   r  r  r9  rp  r`  r   r}  r  r  s
             r0   test_location_scalez"TestLevyStable.test_location_scale  s      lg-W'X=R=T=TUV=W2W  	P45==KNOOO* 0;,/:,tG}-.-8[[*~%%%%%)U]]E!!8I8M 	 XCL''*GFO1!
 
 
 	GDM400000r2   zmethod,decimal_placesrR  r   r\  c           	         t          j        g d          }t          j        g d          }t          j        g d          }t          j        d          5  t                      5 }|                    t
          d           |t          j        _        t          j        	                    |d|dd	
          }t          ||||           ddd           n# 1 swxY w Y   ddd           dS # 1 swxY w Y   dS )z sample points extracted from Tables and Graphs of Stable
        Probability Density Functions - Donald R Holt - 1973 - p 187.
        )r   r   r   r   r   r   r   r   rd   rd   rd   rd   r   r   r   r   r   r   r   r   )gtF_?gܵ|?gQ?g@?gec]?gHP?gPkw?g!rh?gTN?g?gDioɴ?g r?gH?g+?gHPs?gX ?g&?g0*?gv/?ga2U0*?)r   r   ry   r   r   r   ry   r   r   r   ry   r   r   r   ry   r   r   r   ry   r   r5  rB  zDensity calculation unstable.*)categorymessager   r   re  N)rg   r   rD  r   rP   r{  r6   r$  ru  rf   r   )rp   r  decimal_placesxsdensitybetasr~  rf   s           r0   'test_pdf_alpha_equals_one_beta_non_zeroz6TestLevyStable.test_pdf_alpha_equals_one_beta_non_zero  s    XHHH
 
 (  
 
   
 
 [X&&& 
	 
	(9(;(; 
	sJJ'8     4:E0#''AuA1'EECWnf  
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	s7   C/'A$CC/C	C/C	C//C36C3zparams,expected)r0  r1  r   r   )rd   r  r]   r  )r]   r  r   r   c                     t           j                             |d         |d         |d         |d         d          }t          ||           d S )Nr   r   rd   r   rW  r  )r6   r$  r   )rp   paramsrU   observeds       r0   r\  zTestLevyStable.test_stats:  sU     $**1IvayfQivay + 
 
 	Hh/////r2   r  )r   ry   rc  zfunction,beta,points,expectedrU  r  r]   r~   r  r  c                     d|cxk     rdk     sn J t           ||||          t          j        t          |          |                     dS )a\  Ensure the pdf/cdf routines do not return nan outside support.

        This distribution's support becomes truncated in a few special cases:
            support is [mu, infty) if alpha < 1 and beta = 1
            support is (-infty, mu] if alpha < 1 and beta = -1
        Otherwise, the support is all reals. Here, mu is zero by default.
        r   r   )r  r  N)r   rg   r  r  )rp   r  r  r  r  rU   s         r0   !test_distribution_outside_supportz0TestLevyStable.test_distribution_outside_supportH  se    P 5}}}}1}}}}}}HV5t444GCKK**	
 	
 	
 	
 	
r2   N)#r   r   r   r   r  r  r  r  r   r   r  r  rK  r*  r  r  r@  rC  rF  rJ  rg   rZ  r   r  r  r  r  r  r  r\  r6   r$  rn   rf   r  r8   r2   r0   r
  r
    s       ^  ^B ^) ) ^)V ^  ^ [FLlfl4v{7GHHH
 
 [/$>>[CCC  []VV,<==  >=  ?> $ [[Vc1X..
 
 /. 
- - -0 [>??[ 	
  [D$< 
 
   @?

, 
, 
,	, 	, 	,
G 
G 
G [*FL

 
 FL(((###(((k&	   FLDDDCB''B2&&k'	  -
 * + *B [*FL

 
 FL(((###(((k&	   FLDDDCB''B2&&k'	  -
 *y y+ *yv [Wq!f--[VeU^441 1 54 .-1@ [AJ!	
   @ [!RVRVRV!<=/	
 0 0 0 [W&7&7&788[' !%CB''	 !%CB''	 !%Ar2&&	 !%Ar2&&	'	
 :
 
;  98<
 
 
r2   r
  c                       e Zd Zd Zd ZdS )TestArrayArgumentc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestArrayArgument.setup_methodx  r7  r2   c                     t           j                            t          j        d          t          j        d          d          }t          |j        d           d S )Nr   r  r(  )r6   r  r   rg   r  r  r   rC  rp   r   s     r0   test_noexceptionz"TestArrayArgument.test_noexception{  sK    jnn")A,,rwqzz")  + +SY(((((r2   N)r   r   r   r6  r  r8   r2   r0   r  r  w  s2          ) ) ) ) )r2   r  c                       e Zd Zd Zd ZdS )TestDocstringc                    t           j        j        2t          dt           j        j                                        v            t           j        j        4t          dt           j        j                                        v            d S d S )Nr)  r  )r6   r)  r7  r	   lowerr  ru   s    r0   test_docstringszTestDocstring.test_docstrings  sn    >!-J%."8">">"@"@@AAA?".K5?#:#@#@#B#BBCCCCC /.r2   c                 R    t          j                     t          j                     d S rs   )r6   rC   rB   ru   s    r0   test_no_name_argzTestDocstring.test_no_name_arg  s&    r2   N)r   r   r   r  r  r8   r2   r0   r  r    s5        D D D    r2   r  c                     t          g d          } t          | dk    | d          \  }}t          |g d           t          |dg           t          ddk    | d          \  }}t          ||            t          |dgt          j        |           z             t          | dk    | d          \  }}t          ||            t          |dgt          j        |           z             d S )N)r   r   rd   r   rd   r   r   r   rd   )r   rd   rd   r   r   r   )r   r   r   rg   r   r.   r/   r  s      r0   test_args_reducer    s    ###$$Aa!eQ""DAqq///***q1#a!eQ""DAqq!q1#

*+++a!eQ""DAqq!q1#

*+++++r2   c                   R   e Zd Zg dZd Zg dZej                            de	          d             Z
d Zd Zd Zd	 Zd
 Zd Zd Zej        j        ej                            dddg          d                         Zej                            dddg          d             ZdS )TestFitMethod)ncfr  r  c                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestFitMethod.setup_method  r7  r2   )r  r  rT  z	dist,argsc                 t   || j         v rt          j        d|z             t          j        dddddt          j        g          }t          j        dddddt          j        g          }t          t          |          }t          t          |j        |d           t          t          |j        |d           d	S )
r3  z"%s fit known to fail or deprecatedr  r  r  r  r  r   r  N)fitSkipNonFiniter   r   rg   r   r  r  r,  r6   r?  r  r   )rp   r?   r.  r\   r  distfuncs         r0   !test_fit_w_non_finite_data_valuesz/TestFitMethod.test_fit_w_non_finite_data_values  s     4(((K<tCDDDHfffffbfEFFHfffffbfEFF5$''j(,!<<<<j(,!<<<<<<r2   c           
         t           j                            d           t          j        d          5  t          j                            dddd          }t          j        t          j        |          t          j        d          z
  d	z  	                                          }t          t          j        t          j                            |d
d                    |d
dgd           d d d            d S # 1 swxY w Y   d S )Ni90  r5  r  r   r~         4@r  r:  rd   r   r>  r  r   )rg   r   r   rD  r6   r&  r   r)  r  r|  r   r   r   )rp   r\   expected_shapes      r0   test_fix_fit_2args_lognormz(TestFitMethod.test_fix_fit_2args_lognorm  s>   
	u[X&&& 	@ 	@!!$Dr!::AWrvayy26"::'=&A%G%G%I%IJJNBHU]%6%6qq%6%L%LMM+Q3$@ @ @ @	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@s   B;C==DDc                    t          j        dd          }t          j                            |          \  }}t          |d           t          |t          j        d                     t          j                            |d          \  }}t          |d           t          |t          j        d                     t          j                            |d          \  }}t          |d           t          |d           d S )Nr   r  r   rd   r   r  )rg   r  r6   r  r   r   r)  r   rp   r\   rb   rc   s       r0   test_fix_fit_normzTestFitMethod.test_fix_fit_norm  s    IaOOZ^^A&&
UC###E271::...Z^^AA^..
US!UBGAJJ'''Z^^Aa^00
UC###UAr2   c                    t          j        dd          }t          j        |                                          }d}t          j                            ||          \  }}}t          j        |                                          |z
  }t          t          j        |          t          j	        |          z
  |d           t          ||           t          ||                                |z  d           d}d}t          j                            |||          \  }}}t          ||           t          ||           t          ||                                |z  d           d	}d}t          j                            |||          \  }}}t          ||           t          ||           t          ||                                |z  d           d}d	}	t          j                            |||	
          \  }}}t          ||           t          ||	           |t          j        |	          z
  }
t          t          j	        |          |
           d S )Nr   r  r   r   r   rX  r?  r   r   rd   r>  )rg   r  r  r|  r6   rZ  r   r   r   digammar   )rp   r\   meanlogr   r.   rb   rc   rL   r   r   r  s              r0   test_fix_fit_gammaz TestFitMethod.test_fix_fit_gamma  s   IaOO&)).."" 553F16688w&BF1II(:(::AqIIIIS$E16688A:q9999
 bt<<3QS$E16688A:q9999bt<<3QS$E16688A:q9999 VDD3S$UF###bfVnn$GOA..22222r2   c           	         d }t          j        g d          }t          j                            |dd          \  }}}}t          |d           t          |d           t           ||||          ddgd           t          j        g d          }t          j                            |ddd	          \  }}}}t          |d           t          |d           t          |d            ||||          \  }}t          |dd
           d|z
  }	t          j                            |	ddd          \  }
}}}t          |d           t          |d           t          |d            ||
||	          \  }}t          |dd
           t          |
|           t          t          t          j        j        |dd           t          j        g d          }t          t          t          j        j        |dd           t          t          t          j        j        |ddd           t          t          t          j        j        |ddd           t          t          t          j        j        |dddd           d S )Nc                 h   t          |          }t          j        |                                          }t          j        d|z
                                            }t	          j        | |z             }||| t	          j        |           z   z  z
  ||| t	          j        |          z   z  z
  g}|S r   )r  rg   r  rn  r   psi)r.   r/   r\   rv  s1r  psiabr   s           r0   mlefuncz0TestFitMethod.test_fix_fit_beta.<locals>.mlefunc  s     AAB!""BKA&&Eufw{1~~566ufw{1~~5668DKr2   )r
  r   ry   r   r   r>  r  r   rd   )r   r   r   r  )r  r   r   ry   ry  )r   r   r   )r   r   r  r   )r   r  r   r   )
rg   r   r6   r  r   r   r   r   r?  r  )rp   r  r\   r.   r/   rb   rc   dadbr  r  b2r  r  r  s                  r0   test_fix_fit_betazTestFitMethod.test_fix_fit_beta  s   		 		 		 H'''(( :>>!!A>>>1c5S!UA1a((1a&t<<<< H'''(( :>>!!>DD1c5QS!UAAq!!BAD)))) U$z~~bQQq~IIBfRT1VQR$$BAD))))B""" 	j%*.!#aHHHHHZZZ  j%*.!!AFFFFj%*.!!A!LLLLj%*.!!A!LLLL 	j%*.!aQ	( 	( 	( 	( 	( 	(r2   c                    t          j        g d          }t          j                            |          \  }}t          |d           t          |d           t          j                            |d          \  }}t          |d           t          |d           t          j                            |d          \  }}t          |d           t          |d           d S )N)rd   rd   r   r   r   r   r   r?  rd   r   r  r   r   r   )rg   r   r6   r  r   r   r  s       r0   test_expon_fitzTestFitMethod.test_expon_fit(  s    H---..[__Q''
US!UA[__Qq_11
US!UA[__QQ_//
US!UAr2   c           	         t          j        g d          }t          j        |dz
            }t          j                            |d          \  }}}t          ||                                d           t          |d           t          |t          j	        |
                                          d           t          j                            |dd          \  }}}t          |t          j        |t          j        d          z
  dz  
                                          d           t          |d           t          |d           t          j                            |dd	
          \  }}}t          |d	           t          |d           t          |t          j	        |
                                          d           d S )N)r  r   r]   r>     r  r   r   r  r   r  r>  rd   rc  )r   fix_s)rg   r   r  r6   r&  r   r   r}  r   r   r|  r)  )rp   r\   lnxm1rC  rb   rc   s         r0   test_lognorm_fitzTestFitMethod.test_lognorm_fit7  s   H---..q1u!M--aa-88sEuyy{{7777S!rvejjll33%@@@@!M--aa-BBsErw):Q(>'D'D'F'FGG"	$ 	$ 	$ 	$S!UA!M--aat-DDsEUD!!!S!rvejjll33%@@@@@@r2   c                    t          j        g d          }t          j                            |          \  }}t          ||                                           t          ||                                           t          j                            |d          \  }}t          |d           t          ||                                           t          j                            |d          \  }}t          |d           t          |d           t          t          t          j        j        |d           t          t          t          j        j        |d           d S )N)rU  rW  r        "@r   r   r]   r  r}   rV  )rg   r   r6   rT  r   r   r  r9  rj  r?  r  r  s       r0   test_uniform_fitzTestFitMethod.test_uniform_fitK  s#   H)))**]&&q))
US!%%''"""UAEEGG$$$]&&qq&11
US!UAEEGG$$$]&&q&44
US!UBj%-"3QSAAAAj%-"3QsCCCCCCr2   r  MLEMMc           
      `   d\  }}t           j                            ||dd          }t           j                            |d|          }t           j                            |d|          }t	          ||dd	           t           j                            |d|
          }t	          ||dd	           t           j                            |d|          }t           j                            |d|          }t	          ||dd	           t           j                            |d|          }t	          ||dd	           t          t          t           j        j        |dd|           t          t          t           j        j        |dddd|           t           j                            |ddd|          }	|	\  }
}}}t          |
||gg d           d}t           j                            |d          }t           j                            |||          \  }
}}t          |
|           d S )N)rV  r  r^   r4  r  rV  )r   r  )r  r  r  r   )r  r  r  )r  r  )r%  r  )r$  r  r   rd   )r  r   r  r   r   )r  r  r   r   r  )r  r   r   r  )rV  r   r   r:  )	r6   r  r   r   r   r?  r  r   rZ  )rp   r  r.   r/   r\   res_1res_2res_3res_4res_5aabbr"  ssr   s                  r0   test_fshapeszTestFitMethod.test_fshapes]  s   
 1JNN1acN==
qR77
qR77u5u====
q6::u5u====
qR77
qR77u5u====
q6::u5u==== 	j%*.!aOOOO 	j%*.!aQv	7 	7 	7 	7
 
qRa&IIBBb"b\:::... {qs++[__Ta_??
BRr2   c                     t           j        }|                    dd          }t          d          }t	          t
          |j        |fi |d|i d S )Nrd   r^   )rD  r   i)enikibenikir  )r6   rC  r   r  r?  r  r   )rp   r  r?   r   r-  s        r0   test_extra_paramszTestFitMethod.test_extra_params  s]     xx!#x&&t$$$i4FF3FFvFFFFFFr2   N)r   r   r   r   r6  r  r   r   r   r   r  r  r  r  r  r  r  r  r  r  r  r8   r2   r0   r  r    sV       $$$D   433[[(33= = 43=@ @ @  $3 $3 $3L5( 5( 5(n  A A A(D D D$ [[Xt}55$ $ 65 $L [Xt}55G G 65G G Gr2   r  c                   D    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
S )
TestFrozenc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestFrozen.setup_method  r7  r2   c                    t           j        }t          j        dd          }|                    d          }|                    ddd          }t          ||           |                    d          }|                    ddd          }t          ||           |                    d          }|                    ddd          }t          ||           |                    d          }|                    ddd          }t          ||           |                    d          }|                    ddd          }t          ||           |                                }|                    dd          }t          ||           |	                                }|	                    dd          }t          ||           |
                                }|
                    dd          }t          ||           |                                }|                    dd          }t          ||           |                                }|                    dd          }t          ||           |                    d          }|                    ddd          }t          ||           t          |j        |j                   t          |j        |j                   d S )Nr  rV  ra   r  r   rd   )r6   r  rf   r   rn   r  r  r  r  r|  r  r}  rE   r  r.   r/   )rp   r?   frozenresult_fr  s        r0   r  zTestFrozen.test_norm  s   zC000::d##$D44Xv&&&::d##$D44Xv&&&::d##$D44Xv&&&::d##$D44Xv&&&99T??4s33Xv&&&==??S11Xv&&&;;==t3//Xv&&&::<<d#..Xv&&&::<<d#..Xv&&&>>##$c22Xv&&&==##QD44Xv&&&VXtv&&&VXtv&&&&&r2   c                    d}t           j        }t          j        |          }|                    d          }|                    d|          }t          ||           |                    d          }|                    d|          }t          ||           |                    d          }|                    d|          }t          ||           |                    d          }|                    d|          }t          ||           |                    d          }|                    d|          }t          ||           |                                }|                    |          }t          ||           |	                                }|	                    |          }t          ||           |
                                }|
                    |          }t          ||           |                                }|                    |          }t          ||           |                                }|                    |          }t          ||           |                    d          }|                    d|          }t          ||           t          |j        |j        j                   t          |j        |j        j                   d S )Nr}   r  r   r  rd   )r6   rZ  rf   r   rn   r  r  r  r  r|  r  r}  rE   r  r.   r?   r/   )rp   r.   r?   r  r  r  s         r0   
test_gammazTestFrozen.test_gamma  sa   {Q::d##$""Xv&&&::d##$""Xv&&&::d##$""Xv&&&::d##$""Xv&&&99T??q!!Xv&&&==??QXv&&&;;==1Xv&&&::<<!Xv&&&::<<!Xv&&&>>##aXv&&&==##Q""Xv&&&VXv{}---VXv{}-----r2   c                     t          j        d          }|                    d          }|                     d           |                    d          }t          ||           d S )Nr   rd   rW  rX  )r6   r&  r  r   )rp   r  m1r  s       r0   test_regression_ticket_1293z&TestFrozen.test_regression_ticket_1293  sa    q!!]]1V$$$ ]]1 	Rr2   c                 l   d}t          j        |          }|j                            |          \  }}t	          ||gddg           d}t           j                            d|           t	          |j                            |          dt          j        g           d}t          j        |          }|j                            |          \  }}t	          ||gddg           d}t           j                            d|           t	          |j        j        |j        j	        ft           j                            |                     t          j        d          }t          |j        |j        u           dD ]}t          j        |          }t          j        |          }|j        |j	        }}t	          |d           t          t          j        |                     t          j        d          }t           j                            |          \  }}t          ||gdd	g           d S )
Nr  rO  r~   r  rZ   r   rH  rI  ry   )r6   rJ  r?   rK  r   rf   rg   r  r.   r/   r	   r   rL  r   )rp   r  rQ  r.   r/   rv1s         r0   rM  zTestFrozen.test_ab  s    _q!!!w##A&&1aVb#Y'''A###RW))!,,q"&k:::_q!!!w##A&&1aVb#Y'''Aq!!!bgi+U_-I-I!-L-LMMMo$$$'(((  
	/ 
	/A
1A1%%%B4qABBKNN### 
3A?//22DAqQFRI....
	/ 
	/r2   c                 T    t          t          t          j        d                     d S )N	rv_frozen)r	   r-   r6   r7   ru   s    r0   test_rv_frozen_in_namespacez&TestFrozen.test_rv_frozen_in_namespace9  s#    +[99:::::r2   c                    t          j                    }t          t          |d                     d|_        t          |j                                        t          j        	                    d                                                     t          j        	                    d          }|
                    d|           d S )Nr   *   r4  r?  r  )r6   r  r	   r-   r   r   	get_staterg   r   RandomStater   )rp   r  rndms      r0   test_random_statezTestFrozen.test_random_state=  s    //000 !V(2244Y**2..88::	< 	< 	< y$$T**


-----r2   c                    t          j        dd          }t          j        d          }t          j        g dg df          }|||fD ]}d|_        |                    d	           t          j        |          }|                    d	          }t          j        |          }|                    d	          }t          ||           |
                    d
          |
                    d
          g}	t          |	d         |	d                    t          |                    |	d                   |                    |	d                              d S )Ngdsz@g@e?rV  )r   r   rd   r   rV  r  r4  r?  r:  ry   r   r   )r6   r  r  rB   r   r   pickledumpsloadsr   r  rn   )
rp   r  poissr  distfnrL   r0	unpickledr1medianss
             r0   test_picklingzTestFrozen.test_picklingK  s[    z,.ABBb!!"<<<+?+?+?+A B B B UF+ 	4 	4F"&FJJAJV$$A##BQIA&&BR    zz#	c(:(:;GWQZ000GAJ//"wqz224 4 4 4	4 	4r2   c           
         d }t          j        ddd          }t          j        dd          5  |                    |ddd	
          }t           j                            |dddddd	          }d d d            n# 1 swxY w Y   t          ||           t          j        dd          }|                    |          }t           j                            |dd          }t          ||           d S )Nc                     | S rs   r8   r   s    r0   r   z$TestFrozen.test_expect.<locals>.funcf  s    Hr2   rd   r   r   )r.   rb   rc   r5  )r7  divider   T)r   ubconditionalrd   r.  rb   rc   r   r  r  r.  )r   r.  rb   )r6   rZ  rg   rD  r   r   r  )rp   r   gmgm_val	gamma_valrw  p_valpoisson_vals           r0   test_expectzTestFrozen.test_expectc  sQ   	 	 	 [1!1---[(;;; 	I 	IYYtaTYBBF**4d./A4 + I II	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 		***M!###m**4d*BB{+++++s   A A==BBN)r   r   r   r6  r  r  r  rM  r  r  r	  r  r8   r2   r0   r  r    s          1' 1' 1'f2. 2. 2.h  */ */ */X; ; ;. . .4 4 40, , , , ,r2   r  c                   b    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd Zd Zd ZdS )
TestExpectc                 @   t           j                            d dd          }t          |dd           t           j                            d dd          }t          |dd           t           j                            d	dd          }t           j                            d
dd          }t           j                            d dd||          }t          |dd           t           j                            d dd||d          }t          |dd           d S )Nc                     | dz
  | dz
  z  S )Nr   r8   r   s    r0   rM   z&TestExpect.test_norm.<locals>.<lambda>|  s    1qs r2   r   rd   ra   r   r  rX  c                     | S rs   r8   r   s    r0   rM   z&TestExpect.test_norm.<locals>.<lambda>  s     r2   r   r  c                     dS r   r8   r   s    r0   rM   z&TestExpect.test_norm.<locals>.<lambda>      Q r2   rb   rc   r   r  r  c                     dS r   r8   r   s    r0   rM   z&TestExpect.test_norm.<locals>.<lambda>      a r2   Trb   rc   r   r  r  rU  )r6   r  r   r   r  )rp   rA  r@  r   r  prob90prob90cs          r0   r  zTestExpect.test_norm{  s   J33!DDAq"----Jmm!<<Aq"----Z^^Daq^11Z^^Daq^11"";;AQ2""MMFC4444*##KKQaB204 $ 6 6GR444444r2   c           	      R   t           j                            d ddd          }t          |dd           t           j                            d	 dd
d          }t          |dd           t           j                            ddddd          }t           j                            ddddd          }t           j                            d dd
d||d          }t          |dd           t           j                            d ddd||d          }t          |dd           d S )Nc                     | dz
  | dz
  z  S )NUUUUUU@r8   r   s    r0   rM   z&TestExpect.test_beta.<locals>.<lambda>  s    51U7(; r2   r  r   rd   )r.  rb   rc   qq?r  rX  c                     | S rs   r8   r   s    r0   rM   z&TestExpect.test_beta.<locals>.<lambda>  s     r2   rV  r}   r'  r  r]   ra   r   c                     dS )NrU  r8   r   s    r0   rM   z&TestExpect.test_beta.<locals>.<lambda>  s    R r2   )r]   r]   Fr  r  c                     dS r   r8   r   s    r0   rM   z&TestExpect.test_beta.<locals>.<lambda>  r!  r2   TrU  )r6   r  r   r   r  )rp   rA  r@  r  r   r#  r$  s          r0   	test_betazTestExpect.test_beta  s=   J;;'"#1  . .Avr2222JkkRrJJAub1111Z^^D"baq^99Z^^D"baq^99""<<hB)+ru # N NFC4444*##KKhA*+rt $ M MGR444444r2   c                 T   t           j                             dddd          \  }}t           j                            d dd          }t          ||d	
           t           j                            d dd          }t          ||d
           t           j                            d dddd	          }t          ||d
           dt           j                            dd	gdddd                                          z
  }t           j                            d dddd          }t          ||d	
           t           j                            d ddddd          }t          |dd
           t           j                            d ddd          }	t          |	dd	
           d S )Nr  r]   r?  rV  r.  c                     | S rs   r8   r   s    r0   rM   z+TestExpect.test_hypergeom.<locals>.<lambda>  r  r2   )r  r]   r?  r  r  rX  c                     | dz
  dz  S Nr  rd   r8   r   s    r0   rM   z+TestExpect.test_hypergeom.<locals>.<lambda>  s    adQY r2   r  c                     | dz
  dz  S r0  r8   r   s    r0   rM   z+TestExpect.test_hypergeom.<locals>.<lambda>  s    QrTAI r2   r   )r.  rb   r   r  r   c                     dS r   r8   r   s    r0   rM   z+TestExpect.test_hypergeom.<locals>.<lambda>  s    q r2   r  rW  c                     dS r   r8   r   s    r0   rM   z+TestExpect.test_hypergeom.<locals>.<lambda>  s    1 r2   T)r.  rb   r   r  r  c                     dS r   r8   r   s    r0   rM   z+TestExpect.test_hypergeom.<locals>.<lambda>  s    ! r2   r   )r.  r   r  )r6   rp  r   r   rQ  rn  )
rp   m_truev_truer@  rA  v_bounds	prob_trueprob_boundsprob_bcprob_bs
             r0   test_hypergeomzTestExpect.test_hypergeom  s    ..r2qb.AAO"";;[b"IIAvr2222O""#6#6[') # + +Avr2222 ?))*=*=/:.0Q2 * ? ? 	Hfb9999 eo))1b'2r1!)DDHHJJJ	o,,[[{13b - B BKB???? /((;B,-"$ ) H HGQ3333 ''++, ( 4 4FAr222222r2   c                 $   t           j                            d ddd          }dt           j                            dd          z
  }t	          ||d	           t           j                            d
 ddd          }t	          |dd	           d S )Nc                     dS r   r8   r   s    r0   rM   z)TestExpect.test_poisson.<locals>.<lambda>  s    Q r2   r  r   F)r.  r   r  r   rd   r  rX  c                     dS r   r8   r   s    r0   rM   z)TestExpect.test_poisson.<locals>.<lambda>  s     r2   T)r6   r  r   rn   r   )rp   r9  prob_b_trueprob_lbs       r0   test_poissonzTestExpect.test_poisson  s    m**;;Ta7< + > >))!Q///KbAAAA-&&{{!37 ' 9 9GQ333333r2   c                     t           j        }|                    d          }|                    d           |                    d          }t          ||d           d S )N)r  r  )ry   r  rX  )r6   genhalflogisticr   r   )rp   halflogres1r  s       r0   test_genhalflogisticzTestExpect.test_genhalflogistic  sa     '~~6~**F###~~6~**D$333333r2   c                 
   t          t          j        t          j                            dd                               t          t          j        t          j                            d d                               t          t          j        t          j                            d d                               t          t          j        t          j                            d d                               d S )Nr  Gz?c                     dS r   r8   r   s    r0   rM   z/TestExpect.test_rice_overflow.<locals>.<lambda>       r2   )rI  r  c                     dS r  r8   r   s    r0   rM   z/TestExpect.test_rice_overflow.<locals>.<lambda>  rK  r2   c                     dS Nr   r8   r   s    r0   rM   z/TestExpect.test_rice_overflow.<locals>.<lambda>  rK  r2   )r	   rg   r  r6   ricerf   r   ru   s    r0   test_rice_overflowzTestExpect.test_rice_overflow  s     	EJNN35566777EJ--kk-HHIIJJJEJ--kk-HHIIJJJEJ--kk-HHIIJJJJJr2   c                 (   d\  }}t           j                            d |f          }t          |||dz
  z  t	          j        d|z
            z  d           t           j                            d |f|          }t          |||z   d           d S )	N)r  r   c                     | S rs   r8   rY   s    r0   rM   z(TestExpect.test_logser.<locals>.<lambda>  r!  r2   r  rU  r   r   c                     | S rs   r8   rS  s    r0   rM   z(TestExpect.test_logser.<locals>.<lambda>  r!  r2   r  )r6   r  r   r   rg   r  )rp   rw  rb   res_0res_ls        r0   test_logserzTestExpect.test_logser  s    3##KKqd#;;QVrvb1f~~5E	C 	C 	C 	C ##KKqd#DDus{777777r2   c                     d\  }}t           j                            d ||f          }t           j                            d ||f          }t          |||z
  d           t          ||dz  z
  ||z   d           d S )N)r]  r~  c                     | S rs   r8   r   s    r0   rM   z)TestExpect.test_skellam.<locals>.<lambda>      A r2   r  c                     | dz  S r  r8   r   s    r0   rM   z)TestExpect.test_skellam.<locals>.<lambda>  r  r2   r  r   rd   )r6   rn  r   r   )rp   r,  p2r  r  s        r0   test_skellamzTestExpect.test_skellam  s     B]!!++RH!==]!!..Bx!@@BG%0000RU
BG%888888r2   c           
          d\  }}t           j                            d ||f          }t          |t	          d t          ||          D                       ||z
  z  d           d S )N)r   q   c                     | S rs   r8   r   s    r0   rM   z)TestExpect.test_randint.<locals>.<lambda>  r  r2   c              3      K   | ]}|V  d S rs   r8   r>   r   s     r0   r  z*TestExpect.test_randint.<locals>.<genexpr>  s"      55!A555555r2   r   r   )r6   r@  r   r   rn  r   )rp   lohir   s       r0   test_randintzTestExpect.test_randint  s     Bm"";;R9955uR}}55555bA	O 	O 	O 	O 	O 	Or2   c                 T    t          t          t          j        j        d d           d S )Nc                     | dz  S r  r8   r   s    r0   rM   z&TestExpect.test_zipf.<locals>.<lambda>  s
    q!t r2   r  )r
   r{  r6   r  r   ru   s    r0   	test_zipfzTestExpect.test_zipf  s.    ^UZ%6#^T	+ 	+ 	+ 	+ 	+r2   c                     t           j                            d d          }t           j                            d dddd          }t          ||d	
           d S )Nc                     dS r   r8   r   s    r0   rM   z/TestExpect.test_discrete_kwds.<locals>.<lambda>  rZ  r2   r  r  c                     dS r   r8   r   s    r0   rM   z/TestExpect.test_discrete_kwds.<locals>.<lambda>  rZ  r2   r      r  )r.  maxcount	chunksize	tolerancer  rX  )r6   r  r   r   )rp   n0n1s      r0   test_discrete_kwdszTestExpect.test_discrete_kwds   sd    ]!!++D!99]!!++D+/2 " O OBB//////r2   c                     d }dD ]=}t           j                            d|          }t          | ||          d           >d S )Nc                 H    | dz  d| dz  z  z   d| dz  z  z   d| dz  z  z   | z   S )Nr   r]   r   r  r   r>  rd   r8   r  s    r0   poiss_moment5z-TestExpect.test_moment.<locals>.poiss_moment5
  s8    q52b!e8#bQh.BE9B>>r2   )r   r  r   r  r   )r6   r  r  r   )rp   ru  r  m5s       r0   test_momentzTestExpect.test_moment  se    	? 	? 	?  	? 	?B%%a,,BBb 1 1>>>>>	? 	?r2   c                    t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            d          d	           t          t          j                            d
          d
           d S )NrM  rU  ra   r  r]   rZ   )   r  ry  U   r.  )r   r6   r  r   rZ  r  ru   s    r0   test_challenging_cases_gh8928z(TestExpect.test_challenging_cases_gh8928  s     	
))b)<<bAAA
))b)<<bAAA
))b)<<bAAA***77===--"-55r:::::r2   c           	      t   t           j        }|                    dd          }t          |                    dd          |           t          |                    dddd          |           t          |                    dddd          |d	z             t          |                    ddddd
          |           t          |                    dddd          d           t          |                    dddd          d           t          |                    ddddd
          d           d S )Nr]   r   ra   rQ  r  r  r  r  r  Tr"  r  g433333@g433333rW  )r6   rT  r|  r   r   )rp   r?   r  s      r0   test_lb_ub_gh15855zTestExpect.test_lb_ub_gh15855  sH   }iiBai((!44c:::!bAA3GGG!rBBCGLLL!r04 $ 6 67:	< 	< 	< 	!rBBFKKK!rBBGLLL!r04 $ 6 679	; 	; 	; 	; 	;r2   N)r   r   r   r  r,  r<  rB  rG  rP  rW  r]  re  rh  rr  rw  r{  r}  r8   r2   r0   r  r  v  s        
5 5 5 5 5 5& 3  3  3D	4 	4 	44 4 4K K K
8 
8 
89 9 9O O O+ + +
0 0 0? ? ?; ; ;; ; ; ; ;r2   r  c                   2    e Zd Zd Zd Zd Zd Zd Zd ZdS )TestNctc                     t          j        dd          }t          |                    d          d           t          j        dd          }t	          |                    d          dd           d S )Nr   r   ry   r   g K?r]   rX  )r6   nctr   rn   r   rX  s     r0   test_nc_parameterzTestNct.test_nc_parameter1  sc     Yq!__RVVAYY$$$Yq"BFF1II~rBBBBBBr2   c           	          t           j                            dt          j        dd          d d d f         t          j        ddd                    }t          g dg dg dg          }t          ||d	
           d S )Nr   r   r  rZ   r   )gMp^j?g6].ftv?gȳ'ς?gu?)g!Y<a?g]d1p?go|?g?)gHdY?g2Ԥg?g}o/u?g .mr?r  r   )r6   r  rf   rg   r  rZ  r   r   )rp   r   rU   s      r0   test_broadcastingzTestNct.test_broadcasting9  s    immAryAqqq$w7KQ224 4JJJJJJJJJL M M 	XD111111r2   c                 t    t          j        dd          }t          |                                d           d S )Nr   r   r}   )r6   r  r   r  rX  s     r0   test_variance_gh_issue_2401z#TestNct.test_variance_gh_issue_2401A  s1    
 Yq!__RVVXXs#####r2   c                    t           j                             ddd          \  }}}}t          ||||gt          j        t          j        t          j        t          j        g           t           j                             ddd          \  }}}}t          t          j        |                     t          |||gt          j        t          j        t          j        g           t           j                             ddd          \  }}}}t          t          j        |||g                                                     t          |t          j                   d S )Nr  r  rW  )r  ncrY  r  rX  )r6   r  r   rg   r  r	   r  rB  r  s        r0   test_nct_inf_momentszTestNct.test_nct_inf_momentsI  s	   Y__V_DD
1aaAq\BFBFBFBF#CDDDY__V_DD
1aAaAY 8999Y__V_DD
1aQ1I&&**,,---Qr2   c                    t           j                            dd          }t           j                             dd          }ddg}t          ||d         d           t          ||d           t           j                            dd          }t           j                             dd          }d	d
g}t          ||d         d           t          ||d           d S )Nr   rd   g@ @g*dn?r   r  r   r   gqI  @gL) ?rA  )r6   r  r|  r   )rp   nct_mean_df_1000nct_stats_df_1000expected_stats_df_1000nct_mean	nct_statsrx  s          r0   test_nct_stats_large_df_valuesz&TestNct.test_nct_stats_large_df_valuesV  s     !9>>$22!IOOD!44
 #56H!I(*@*C"	$ 	$ 	$ 	$)+A"	$ 	$ 	$ 	$ 9>>&!,,IOOFA..	,.@A."3%@@@@	>======r2   c           	      ~    t          t          j                            ddt	          d                    d           d S )Nrd   i   r   )r   r6   r  rn   r   ru   s    r0   test_cdf_large_nczTestNct.test_cdf_large_ncl  s0    	aE%LL991=====r2   N)	r   r   r   r  r  r  r  r  r  r8   r2   r0   r  r  0  sq        C C C2 2 2$ $ $     > > >,> > > > >r2   r  c                   &    e Zd Zd Zd Zd Zd ZdS )TestRecipInvGaussc                 V    t           j                            dd          }|dk    sJ d S )Nr   r  r~   )r6   recipinvgaussrf   r  s     r0   test_pdf_endpointz#TestRecipInvGauss.test_pdf_endpoints  s+    ##As++Cxxxxxxr2   c                 l    t           j                            dd          }|t          j         k    sJ d S )Nr   r  )r6   r  r   rg   r  r  s     r0   test_logpdf_endpointz&TestRecipInvGauss.test_logpdf_endpointw  s/    "))!S11wr2   c                 n    t           j                            dd          }d}t          ||d           d S )Nr   ry   g9V9s;r~  r   )r6   r  rn   r   rp   rw  rU   s      r0   test_cdf_small_xz"TestRecipInvGauss.test_cdf_small_x{  s<      ##D#..(8%000000r2   c                 l    t           j                            dd          }d}t          ||d           d S )NP   ry   glH<r`  )r6   r  r  r   r  s      r0   test_sf_large_xz!TestRecipInvGauss.test_sf_large_x  s7    ""2s++(8U+++++r2   N)r   r   r   r  r  r  r  r8   r2   r0   r  r  q  sP            1 1 1(, , , , ,r2   r  c                        e Zd Zd Zd Zd ZdS )TestRicec                    g d}t          t          j        t          j                            |d                                                               t          t          j        t          j                            |d                                                               t          t          j        t          j                            |d                                                               t          t          j        t          j        	                    |d                                                               g d}t          t          j        t          j        
                    |d                                                               t          j                            dd          }t          t          j        |                                                     d}t          t          j                            |d          t          j                            ||          |d	           d S )
N)r  rU  rV  r~   r/   )rZ   rZ   ry   r  r   rW  rX  r  r   )r	   rg   r  r6   rO  rf   rB  r   rn   r  r  r   )rp   r\   r  rW  r/   s        r0   test_rice_zero_bzTestRice.test_rice_zero_b  s   MMEJNN1N334488::;;;EJ--a2-6677;;==>>>EJNN1N334488::;;;EJ--a2-6677;;==>>>   EJNN1N334488::;;;z622D!!%%''(((
 
q!,,ejnnQ.B.BQ	( 	( 	( 	( 	( 	(r2   c                     t           j        j        }t           |d          j        d           t           |dd          j        d           d S )NrV  r  r   )r   r   )r/   r   )r6   rO  r   r   r   rC  r  s     r0   test_rice_rvszTestRice.test_rice_rvs  sO    jnSS2YYY^Q'''SS2F+++16:::::r2   c                    t           j                            t          j        ddd          t          j        ddd                    }g d}t          ||           t          j        ddd          }t           j                            |dd          }g d	}t          ||           t          j         j                            d
t          j        ddd                    }g d}t          ||           d S )Nr]      )g/Ƹ?g[jǊ\?g 	?g9LJ?g#O?gXx?glO?g٥a%?gVzӯ?gTQ+xQ?g?`J?go?gbu=?gIo|?g"Z6?rZ   r   g     @_@r   r  )	g<~@gwd
@gC?@gb
0@g` A@@g'NxP@g33-a@g4pv@g$F@ry      )gJ-$@g+f4@gce*D>@g$D@gnHGI@grN@g<
uQ@giff T@g9r[V@g3bXQ Y@gqxJ[@g`*DD ^@g@`@gdAa@)r6   rO  rn   rg   r  r   r  r5   )rp   rn   cdf_expprobabilitiesr  ppf_exps         r0   test_rice_gh9836zTestRice.test_rice_gh9836  s     jnnRYr333RYr35K5KLLO O O
 	W%%%	#q#..jnn]En;;L L L 	W%%%k""3	"c2(>(>??; ; ;
 	W%%%%%r2   N)r   r   r   r  r  r  r8   r2   r0   r  r    sA        ( ( (*; ; ;
'& '& '& '& '&r2   r  c                        e Zd Zd Zd Zd ZdS )
TestErlangc                 D    t           j                            d           d S r3  r5  ru   s    r0   r6  zTestErlang.setup_method  r7  r2   c           	         t          j                    5  t          j        dt                     t	          t          t
          j        j        dddd           g d}t
          j                            |d          }t
          j	                            |d          }t          ||d	
           d d d            d S # 1 swxY w Y   d S )Nrt  r  r   r   r   r(  )ry   rU  r}   r  r  r_  r   )rx  ry  rz  r{  r?  r6   erlangr   r   rZ  r   )rp   r   result_erlangresult_gammas       r0   test_erlang_runtimewarningz%TestErlang.test_erlang_runtimewarning  s     $&& 	D 	D!'>::: .,*CQaaI I I I (''D!L,,Ta,88M ;??4A?66LM<dCCCC	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	Ds   BB==CCc                     t          t          j                            dddg          t          j                            dddg                     d S )Nry   r   r   r  )r   r6   r  rf   rZ  ru   s    r0   test_gh_pr_10949_argcheckz$TestErlang.test_gh_pr_10949_argcheck  sR    U\%%caW%55[__SQG_44	6 	6 	6 	6 	6r2   N)r   r   r   r6  r  r  r8   r2   r0   r  r    sD          D D D&6 6 6 6 6r2   r  c                       e Zd Zd Zd Zd Zej                            dddg          d             Z	ej                            ddd	gd
dgg          d             Z
d Zd ZdS )TestRayleighc                 D    t           j                            d           d S )Nr'  r5  ru   s    r0   r6  zTestRayleigh.setup_method  s    
	y!!!!!r2   c                 d    t           j                            d          }t          |d           d S )Nr<  g)Zx)r6   r)  r   r   rp   r  s     r0   r\  zTestRayleigh.test_logpdf  s.    N!!"%%./////r2   c                 d    t           j                            d          }t          |d           d S )Nr<  i)r6   r)  rw  r   r  s     r0   r  zTestRayleigh.test_logsf   s-    N  $$5!!!!!r2   r  )gB)Q?got|?)gS2P?g3?c                    t           j                            d||          }d } |||          }t           j                            ||          \  }}t	          ||           t	          ||           t           j                            |d          \  }}t	          |d           t           j                            |          \  }}t	          | |||                     d S )Nr  r  c                 b    t          j        | |z
  dz            dt          |           z  z  dz  S )Nrd   ry   )rg   rn  r  )r   r   s     r0   r  z(TestRayleigh.test_fit.<locals>.scale_mle	  s/    FD4KA-..!c$ii-@RGGr2   r   r  r  )r6   r)  r   r   r   )rp   r   r   r   r  scale_expectrb   rc   s           r0   r  zTestRayleigh.test_fit  s     ~!!sy!II	H 	H 	H !yw//^''7';;
US'"""UL))) ^''R'88
UUB
 ^''--
UUIIdC0011111r2   rI  r{   g̡=E?g@1d?c                 ~    t           j                            d||          }t          t           j        |           d S )Nr  r  )r6   r)  r   r   )rp   r   r   r   s       r0    test_fit_comparison_super_methodz-TestRayleigh.test_fit_comparison_super_method  s8    
 ~!!sy!II%end;;;;;r2   c                 8    t          t          j                   d S rs   )r  r6   r)  ru   s    r0   r@  zTestRayleigh.test_fit_warnings%  s    EN+++++r2   c                    t           j                            d          }d\  }}}t          j                            ||||          }t          j                            |          \  }}|t          j        |          k     sJ t          j                            ||          \  }}|t          j        |          k     sJ ||k    sJ d S )Ni  )r<  r  ra  r  r  )rg   r   r   r6   r)  r   r   r  )	rp   r   rb   rc   r   r   r   r   r   s	            r0   test_fit_gh17088zTestRayleigh.test_fit_gh17088(  s     i##C(('UDn  e$S II^'',,
$$$$"^//E/BB$$$$E!!!!!!r2   N)r   r   r   r6  r\  r  r   r   r   r  r  r@  r  r8   r2   r0   r  r    s        " " "0 0 0" " " [03K3K3M N N2 2N N2. [0D$<4>
3K3M N N< <N N<, , ,
" 
" 
" 
" 
"r2   r  c                       e Zd Zd Zd Zd Zej                            dg d          d             Z	ej                            dg d          d	             Z
d
S )TestExponWeibc                     d}d}d}t           j                            |||          }t           j                            |||          }t	          ||gddg           d S )NrZ   rU  r   g:23W+g~`9k)r6   	exponweibrf   r   r   )rp   r\   r.   r  rw  r[  s         r0   test_pdf_logpdfzTestExponWeib.test_pdf_logpdf7  ss    O1a((%%aA..D	/1DE	G 	G 	G 	G 	Gr2   c                 ~   t          j        ddd          }d}d}t          j                            |||          }t          j                            ||          }t          ||           t          j                            |||          }t          j                            ||          }t          ||           d S )Nr  r   r   r   r^   )rg   r  r6   r  rf   weibull_minr   r   rp   r\   r.   r  rw  rU   r[  s          r0   test_a_is_1zTestExponWeib.test_a_is_1B  s     KB""O1a(($((A..8$$$%%aA..$++Aq11h'''''r2   c                 z   t          j        ddd          }d}d}t          j                            |||          }t          j                            |          }t          ||           t          j                            |||          }t          j                            |          }t          ||           d S )NrO  r   r]   )rg   r  r6   r  rf   r  r   r   r  s          r0   test_a_is_1_c_is_1z TestExponWeib.test_a_is_1_c_is_1R  s    KAr""O1a((;??1%%8$$$%%aA..;%%a((h'''''r2   zx, a, c, ref))r   r  rc  g=J ?)r<  r  rc  g$+PR>)r  r  rc  g><)r  r  rc  ggX.X:)r        ?rc  gRy9)r   r  rV  g'vR0=)g_QPr  ri  gQ:<c                 l    t           j                            |||          }t          ||d           d S r  )r6   r  r  r   )rp   r\   r.   r  r  r  s         r0   r  zTestExponWeib.test_sfq  s8     _1a((Ce,,,,,,r2   zp, a, c, ref))r   r  rc  g;y$(@)gMg<r  rc  gdbq^@)r  r   rd   gE@)gvIh%L=r  r   g/7@)r  r  ri  gTWTOc                 l    t           j                            |||          }t          ||d           d S r  )r6   r  r  r   )rp   rw  r.   r  r  r  s         r0   r  zTestExponWeib.test_isf  s8     o!!!Q**Su------r2   N)r   r   r   r  r  r  r   r   r   r  r  r8   r2   r0   r  r  5  s        	G 	G 	G( ( ( ( ( (> [	5 	5 	5	 	- -	 	-* [	4 	4 	4 . . . . .r2   r  c                       e Zd Zd Zd ZdS )TestFatigueLifec                 j    t           j                            dd          }t          |dd           d S )Nr  r  X9r   r   )r6   r  r  r   r  s     r0   test_sf_tailzTestFatigueLife.test_sf_tail  s8       ,,0u======r2   c                 n    d}t           j                            |d          }t          |dd           d S )Nr  r  r  r   r   )r6   r  r  r   )rp   rw  r  s      r0   test_isf_tailzTestFatigueLife.test_isf_tail  s:    !!!!S))5u------r2   N)r   r   r   r  r  r8   r2   r0   r  r    s2        > > >. . . . .r2   r  c                       e Zd Zd Zd Zej                            dddg          d             Zd Z	ej                            dd	d
g          d             Z
dS )TestWeibullc                 f    t           j                            dd          }t          |d           d S r  )r6   r  r   r   r  s     r0   r\  zTestWeibull.test_logpdf  s0    $$Q**Qr2   c                    d}d}d}t           j                            |||          }t          |t	          j        d          dz             t           j                            |||          }t          |dt	          j        d          z
             t           j                            |||          }t          |t          j
        d                      t           j                            |||          }t          |t	          j        t          j
        d                                t           j                            |||          }t          |t	          j        d                     t           j                            |||          }	t          |	d           t           j                            ddd          }t          |t	          j        d	                     t           j                            ddd          }	t          |	d	           d
}t           j                            |||          }t          |t	          j        d          dz             t           j                            |||          }t          |dt	          j        d          z
             t           j                            |||          }t          |t	          j        d                     t           j                            |||          }t          |d           t           j                            |||          }t          |t          j
        d                      t           j                            |||          }	t          |	t	          j        t          j
        d                                t           j                            ddd          }t          |t          j
        d                      t           j                            ddd          }	t          |	t	          j        t          j
        d                                d S )Nr  r}   rV  r  r  r   r9  rd   r6  r  g&.gCe )r6   r  rf   r   rg   r   r   r  rn   r   r  r  r  rw  weibull_max)
rp   r\   r.   r/   rw  r  r  lcrL   r%  s
             r0   test_with_maxima_distribz$TestWeibull.test_with_maxima_distrib  s   .  !!!Qa!0026%==?+++%%a!%44EBF1II-...!!!Qa!00GM%000111%%a!%44BFGM%$8$8#899:::  AQ //26%==)))$$Q$33E"""   Qa 0026$<<((($$R!$44D!!! !!!Qa!0026%==?+++%%a!%44EBF1II-...!!!Qa!0026%==)))%%a!%44E"""  AQ //GM%000111$$Q$33BFGM%$8$8#899:::    33GM*@AAABBB$$UAQ$77BFGM2H$I$I#IJJKKKKKr2   rc   rU  rZ   c                 x    t           j                            |dz  |dz  d|          }t          |d           d S )NrP  r?  r   r  g>)r6   r  r/  r   r  s      r0   r0  zTestWeibull.test_delta_cdf  sI    " !,,U3Ya38 - : :566666r2   c                    t           j                            d          }d\  }}}t          j        |||          }|                    d|          }t          j                            |dd          \  }}}	t          j                            |dd          \  }
}}||cxk    rdk    sn J ||
k    sJ t          j                            |ddd	
          \  }}}|dk    sJ t          j        |||          }|                    d          }t          j        |          t          j        |          f}t          ||           d S )Nl   > )rd   r  ry   r^   r  r  r   r   r  r  r   r  rX  )
rg   r   r   r6   r  r   r   r|  r  r   )rp   r   r  rb   rc   r?   r   c2r  r  c3r	  r
  c4r  r  r  r   r  s                      r0   test_fit_minzTestWeibull.test_fit_min$  sT   i##$788#3 C//hhCch22 !,00c0BBD& ,00c0BBD&t    q      Rxxxx !,00a$0OOD&{{{{!"dF33kk$k''gcllEJsOO+S!!!!!r2   r  )r<  r   r  )r   r  gq뮕qH)c                     t          t          j                            ||          |d           t          t          j                            ||          |d           d S r  )r   r6   r  r  r  r  s       r0   r  zTestWeibull.test_sf_isfB  sZ     	),,Q22CeDDDD)--c155quEEEEEEr2   N)r   r   r   r\  r  r   r   r   r0  r  r  r8   r2   r0   r  r    s          
RL RL RLh [WsCj117 7 217(" " "< [[+J,D+E F FF FF FF F Fr2   r  c                       e Zd Zd Zd ZdS )TestDweibullc                 B   t           j                            d          }d|                    dd          z  }t          j                            |          }t          j                            |          t          j        d          z
  }t          ||d           d S )N   q>~). r]   r^   r  ry   r   r   )
rg   r   r   r  r6   dweibullrE   r  r  r   )rp   r   r  r   r  s        r0   rr  zTestDweibull.test_entropyK  s     i##$788

2
...n$$Q''''**RVC[[8Su------r2   c                 P   t           j                            d          }d|                    dd          z  }d|                                z  }t
          j                            ||          }dt
          j                            ||          z  }t          ||d           d S )Nr  r]   r   r  ry   r   r   )
rg   r   r   r  rT  r6   r  r  r  r   )rp   r   r  r\   r   r  s         r0   r  zTestDweibull.test_sfX  s     i##$788


,,,n1%%E%((A...Su------r2   N)r   r   r   rr  r  r8   r2   r0   r  r  J  s2        . . .. . . . .r2   r  c                   D    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
S )TestTruncWeibullc                 r    t           j                            ddgddd          }t          |ddg           d S )NrZ   r}   g)\(?gףp=
?r~   )r6   truncweibull_minrf   r   r  s     r0   test_pdf_boundsz TestTruncWeibull.test_pdf_boundse  s<    "&&Sz3dCCQc
#####r2   c                     t           j                            dddt          j                  }t          |d           t           j                            dddd          }t          |d           d S )Nr}   rU  r~   r  g~?)r6   r  r   rg   r  r   r   r  s     r0   r\  zTestTruncWeibull.test_logpdfj  se    "))#sC@@Q "))#sC==./////r2   c                 r    t           j                            ddgddd          }t          |ddg           d S )Nr~   rU  r}   rZ   )r6   r  r  r   r  s     r0   test_ppf_boundsz TestTruncWeibull.test_ppf_boundsr  s<    "&&Sz3SAAQc
#####r2   c                     g d}t           j                            |ddd          }t           j                            |ddd          }t	          ||           d S N)r~   rZ   r   ry   rc  r  rU  r}   r~   rV  )r6   r  r  rn   r   rp   r  r\   q_outs       r0   test_cdf_to_ppfz TestTruncWeibull.test_cdf_to_ppfw  s[    000"&&q"b"55&**1b"b995!!!!!r2   c                     g d}t           j                            |ddd          }t           j                            |ddd          }t	          ||           d S r  )r6   r  r  r  r   r  s       r0   test_sf_to_isfzTestTruncWeibull.test_sf_to_isf}  s[    000"&&q"b"55&))!RR885!!!!!r2   c                    dddfdt           j                            d          }t          |d           t           j                            d          }t	          fd          \  }}t          ||           t           j                            d          }t	          fd	          \  }}t          ||           t           j                            d
          }t	          fd          \  }}t          ||           t           j                            d          }	t	          fd          \  }
}t          |	|
           d S )Nr}   rU  rV  c                 T    | |z  t           j                            |           z  S rs   )r6   r  rf   )r\   rv  r.   r/   r  s     r0   xnpdfz)TestTruncWeibull.test_munp.<locals>.xnpdf  s)    a4.221aA>>>>r2   r   r   c                      | d          S r   r8   r\   r 	  s    r0   rM   z,TestTruncWeibull.test_munp.<locals>.<lambda>      a r2   rd   c                      | d          S r  r8   r	  s    r0   rM   z,TestTruncWeibull.test_munp.<locals>.<lambda>  r	  r2   r   c                      | d          S rN  r8   r	  s    r0   rM   z,TestTruncWeibull.test_munp.<locals>.<lambda>  r	  r2   r   c                      | d          S )Nr   r8   r	  s    r0   rM   z,TestTruncWeibull.test_munp.<locals>.<lambda>  r	  r2   )r6   r  r  r   r   r   )rp   r<  r  m1_expectedr   r  m2_expectedm3m3_expectedr  m4_expectedr.   r/   r  r 	  s              @@@@r0   	test_munpzTestTruncWeibull.test_munp  s   	? 	? 	? 	? 	? 	? 	? #**1aA66R#**1aA663333Q::QK(((#**1aA663333Q::QK(((#**1aA663333Q::QK(((#**1aA663333Q::QK(((((r2   c                 ^   d}d}d}t          j        dt          j        dt          j        dt          j        d          z              z             z
            }t          j                            ||||          }t          |d           t          j                            ||||          }t          |t          j        d                      t          j        	                    d|||          }t          ||           t          j        
                    ||||          }t          |d           t          j                            ||||          }	t          |	t          j        d                      t          j                            d|||          }
t          |
|           d S )NrU  rV  r}   r   ry   r(  )rg   r)  r  r   r6   r  rn   r   r  r  r  rw  r  )rp   r.   r/   r  x_medrn   r  r  r  r%  r  s              r0   test_reference_valuesz&TestTruncWeibull.test_reference_values  so   BF3"rvbzz/0B)C)C#CDDDEE$((1a88S!!!#**5!Q::RVBZZK((($((aA66U####&&uaA66C   #))%Aq99RVBZZK((($((aA66U#####r2   c                 *   d}d}d}t           j        }d}t          j                            |||          }t          j                            |||||          }t          ||           t          j                            |||          }t          j                            |||||          }	t          ||	           t          j                            |||          }
t          j                            |||||          }t          |
|           t          j        	                    |||          }t          j        	                    |||||          }t          ||           t          j        
                    |||          }t          j        
                    |||||          }t          ||           t          j                            |||          }t          j                            |||||          }t          ||           t          j        
                    dd||d          }t          |t          j        d	                     t          j                            dd||d          }t          |d	           d S )
Nr  r}   r~   rV  r  r9  rd   r   r6  )rg   r  r6   r  rf   r  r   r   rn   r  r  rw  r   )rp   r\   r  r.   r/   rc   rw  p_truncr  lp_truncrn   	cdf_truncr  lc_truncrL   s_truncr%  ls_truncs                     r0   test_compare_weibull_minz)TestTruncWeibull.test_compare_weibull_min  se    F!!!Qe!44(,,Q1au,EE7###%%a%%88)00Aq!50IIH%%%##Aq#66*..q!Q.GG	Y'''%%a%%88)00Aq!50IIH%%%  AU 33(++Aq!Qe+DD7###$$Q$77)//1a%/HHH%%% "%%b!Q%;;26$<<(((#))"aAQ)??D!!!!!r2   c                    d\  }}}t          j        ||d          }t          j                            ||||          }t          j                            ||||          }t          j                            ||          t          j                            ||          z
  }t          j                            ||          |z  }t          j                            ||          t          j                            ||          z
  |z  }	t           j                            ||           t           j                            ||	           d S )N)r  r   r  r^   )	rg   rZ  r6   r  rf   rn   r  testingr   )
rp   r  r.   r/   r\   r  r  r  r  r  s
             r0   test_compare_weibull_min2z*TestTruncWeibull.test_compare_weibull_min2  s    "1aK1c""%))!Q155%))!Q155 $$Q**U->-B-B1a-H-HH $$Q**T1!%%a++e.?.C.CAq.I.II4O

""4...

""4.....r2   N)r   r   r   r  r\  r  r  r  r	  r	  r	  r	  r8   r2   r0   r  r  c  s        $ $ $
0 0 0$ $ $
" " "" " ") ) )6$ $ $0'" '" '"R/ / / / /r2   r  c                       e Zd Zd Zd ZdS )	TestRdistc                     t           j        }g d}t          |                    |                    |d          d          |d           d S )Nr^  g     @r   rX  )r6   rdistr   rn   r  )rp   r  r  s      r0   test_rdist_cdf_gh1285zTestRdist.test_rdist_cdf_gh1285  sX    $$$FJJvzz&%'@'@%HH"A	/ 	/ 	/ 	/ 	/ 	/r2   c                 
   t          j        ddd          }d}t          dt          j        |dz  |dz                                |dz   dz            z  t          j        |                              |                     d S )NgGzr%  r]   g@ry   rd   r   )rg   rZ  r   r6   r  rf   r	  )rp   r\   r  s      r0   test_rdist_betazTestRdist.test_rdist_beta  s    KtR((C
1Q3! 4 4 8 8!a% C CC!KNN..q11	3 	3 	3 	3 	3r2   N)r   r   r   r	  r!	  r8   r2   r0   r	  r	    s2        / / /3 3 3 3 3r2   r	  c                   2    e Zd Zd Zd Zd Zd Zd Zd ZdS )TestTrapezoidc                 V   g d}|D ]}d|dg}t          t          j                            |||          t          j                            ||                     t          t          j                            |||          t          j                            ||                     d S )N)r   r  ry   r   r   r   )r   r6   r   rf   triangrn   )rp   modesmoder\   s       r0   test_reduces_to_triangz$TestTrapezoid.test_reduces_to_triang  s        	; 	;DD!A 3 3AtT B B % 0 0D 9 9; ; ; 3 3AtT B B % 0 0D 9 9; ; ; ;		; 	;r2   c                 b   t          j        ddd          }t          t          j                            |dd          t          j                            |                     t          t          j                            |dd          t          j                            |                     d S Nr   r   r]   )rg   rZ  r   r6   r   rf   rT  rn   r  s     r0   test_reduces_to_uniformz%TestTrapezoid.test_reduces_to_uniform
  s    K1b!!EO//1a88%-:K:KA:N:NOOOEO//1a88%-:K:KA:N:NOOOOOr2   c                 n   t          t          j                            ddd          d           t          t          j                            ddd          d           t          t          j                            ddd          d           t          t          j                            ddd          d           t          t          j                            d	dd          d
           t          t          j                            ddd          d           t          t          j                            ddd          d
           t          t          j                            d	dd          d           t          t          j                            ddd          d           t          t          j                            ddd          d           t          t          j                            ddd          d           t          t          j                            ddd          d           d S )Nr   rd   r   ry   r  rt  r  rU  rZ   g      ?r  r  r  r
  g      ?)r   r6   r   rf   rn   ru   s    r0   
test_caseszTestTrapezoid.test_cases  s   EO//1a88!<<<EO//1a88!<<<EO//Q<</	1 	1 	1EO//S#>>/	1 	1 	1 	EO//S#>>FFFEO//S#>>EEEEO//S#>>FFFEO//S#>>HHHEO//S#>>FFFEO//S#>>DDDEO//S#>>HHHEO//S#>>DDDDDr2   c                   	
 d\  	

	z
  	z
  z  	z
  	z
  z  		z
  f\  }}}}dz   
z
  	z
  z  	
fd} |d          } |d          |dz  z
  }dz
  
z   	z
  z  z   
z
  	z
  z  t          j        dz   
z
  	z
  z            z   }t          t          j                            ||||          |d           t          t          j                            ||||          |d           t          t          j                            ||||          |d           t          t          j                            ddd	d
          dd           t          t          j                            ddd	d
          dd           t          t          j                            ddd	d
          dd           d S )N)r  r   rd   r   rd   c                     | dz   z  | dz   z  z
  z
  z  | dz   z  | dz   z  z
  z
  z  z
  z  | dz   z  | dz   z  S )Nrd   r   r8   )rv  r.   r/   r  drq  s    r0   r  z6TestTrapezoid.test_moments_and_entropy.<locals>.moment*  sn    !ac(Q1X-!A#6!Hq1Q3x/AaC89 :qSqS" #r2   r   ry   r  rX  r   r  r  r   r   )rg   r  r   r6   r   r|  r  rE   )rp   r,  r\  rb   rc   r  r|  r  rE   r.   r/   r  r0	  rq  s            @@@@@r0   test_moments_and_entropyz&TestTrapezoid.test_moments_and_entropy#  s    "
1acac]QqSQqSM1acABU1QqM	# 	# 	# 	# 	# 	# 	# 	# 	#
 vayyfQii$'!1Qq/QqSU1W-sac!eAg0G0GGEO00ReDD "	. 	. 	. 	.EO//BUCC	- 	- 	- 	-EO33BCGG#R	1 	1 	1 	1 	EO00Ar1==r2NNNNEO00Ar1==q"MMMMEO//1b!<<aLLLLLLr2   c                    t          j        g d          }t          j        ddg          d d d f         }t          j        g d          }t          j                            |||          }t          j        |||          \  }}}t          j        |j        |j                  }t          j	        |j                  }	t          |	|                                |                                |                                          D ]+\  }
}}}t          j                            |||          ||
<   ,t          ||                    |j                  d           t          j        t          j                            ||d	                    }t          j        ||          \  }}t          j        |j        d
f          }t          j	        |j                  }	t          |	|                                |                                          D ]+\  }
}}t          j                            ||d	          ||
<   ,t          ||j                            |j                  d           d S )Nr  ry   r  )r  r   r  r  r   r   rW  rX  r   )rg   r   r6   r   rf   broadcast_arraysemptyr   r   r  r  ravelr   r  rC  r   r  )rp   r  r0	  r\   rA  ccddr  r   indr  r  c1d1s                 r0   test_trapezoid_vectz!TestTrapezoid.test_trapezoid_vect>  s
   H___%%Hc3Z  D)H&&&''O1a(((Aq11
Bhrwbh///i   bhhjj"((**bhhjjII 	5 	5MAr2r_((R44CFF3;;qw//e<<<< Ju,,Q6,BBCC$Q**Bh|$$i  S"((**bhhjj99 	C 	CIAr2_**2r6*BBCFF35==11>>>>>>r2   c                     t          j        ddd          }t          t          j                            |dd          t          j                            |                     d S r*	  )rg   rZ  r   r6   rF   rf   rT  r  s     r0   
test_trapzzTestTrapezoid.test_trapzX  sM    K1b!!EKOOAq!44em6G6G6J6JKKKKKr2   N)	r   r   r   r(	  r+	  r-	  r1	  r;	  r=	  r8   r2   r0   r#	  r#	     s|        ; ; ;P P P
E E E(M M M6? ? ?4L L L L Lr2   r#	  c                       e Zd Zd ZdS )
TestTriangc                    t          j        d          5  t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d	           t          t          j                            dd          d           t          t          j                            dd          d
           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           d d d            d S # 1 swxY w Y   d S )Nraiser  r   r}   ry   rU  r   r~   rd   rc  r   )rg   rD  r   r6   r%	  rf   rn   ru   s    r0   test_edge_caseszTestTriang.test_edge_cases_  s   [W%%% 	6 	6))!Q//444))#q112666))!Q//444))!Q//333))#q112666))!Q//333))"b112666))#r22D999))#r22C888))"b112666))#r22D999))"b111555	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6s   H)IIIN)r   r   r   rB	  r8   r2   r0   r?	  r?	  ^  s#        6 6 6 6 6r2   r?	  c                       e Zd Zej                            dddg          d             Zej                            dg d          d             ZdS )	TestMaxwellr  )r  gCR5&.)r{   g7q?c                 d    t          t          j                            |          |d           d S r  )r   r6   maxwellr  r  s      r0   r  zTestMaxwell.test_sfw  s/     	((++Su======r2   r  ))r_  g1!@)g    ?g?)g      <gCuJ!@c                 d    t          t          j                            |          |d           d S r   )r   r6   rF	  r  r  s      r0   r  zTestMaxwell.test_isf  s/    
 	))!,,c>>>>>>r2   Nr  r8   r2   r0   rD	  rD	  r  s        
 [X::<= => >= => [X: : :; ;? ?	; ;? ? ?r2   rD	  c                       e Zd Zd Zd ZdS )
TestMielkec                    d\  }}t          t          j        ||                              d          t          j                   t          t          j        |d                              d          t          j                   t          t	          j        t          j        |d                              d                               d S )N)g rh@gv?r   rU  r  )r   r6   mielker  rg   r  r	   r  )rp   rY   rL   s      r0   rB  zTestMielke.test_moments  s    1U\!Q''..q1126:::U\!S))0033RV<<<ELD1188;;<<=====r2   c                     t          j        ddd          }d\  }}t          t          j                            ||||z            t          j                            |||                     d S )Nr{   r^   r<  )g@gHzG@)rg   rZ  r   r6   burrrf   rK	  )rp   r\   rY   rL   s       r0   test_burr_equivalencez TestMielke.test_burr_equivalence  s^    Kc2&&1
q!QqS115<3C3CAq!3L3LMMMMMr2   N)r   r   r   rB  rN	  r8   r2   r0   rI	  rI	    s7        > > >N N N N Nr2   rI	  c                        e Zd Zd Zd Zd ZdS )TestBurrc           	      n   t           j        ddgt           j        ddgt           j        ddgt           j        ddgt           j        ddgt           j        ddgt           j        d	d
gg}d |D             }d |D             }t	          ||           d |D             }d |D             }t	          ||           d S )N)r   r   )ry   rd   )r   r   )rd   ry   rU  ry   rU  )r   rd   r}   c                 <    g | ]\  }}} |j         |j        g|R  S r8   rh  ri  s       r0   r@   z0TestBurr.test_endpoints_7491.<locals>.<listcomp>  rl  r2   c                     g | ]\  }}}|	S r8   r8   rn  s       r0   r@   z0TestBurr.test_endpoints_7491.<locals>.<listcomp>  rp  r2   c                 <    g | ]\  }}} |j         |j        g|R  S r8   )r   r.   ri  s       r0   r@   z0TestBurr.test_endpoints_7491.<locals>.<listcomp>  s4    @@@<2uayry&&&&@@@r2   c                 >    g | ]\  }}}t          j        |          S r8   )rg   r  rn  s       r0   r@   z0TestBurr.test_endpoints_7491.<locals>.<listcomp>  s)    FFF)=UI26)$$FFFr2   )r6   fiskrM	  burr12r   )rp   r   rs  rt  s       r0   test_endpoints_7491zTestBurr.test_endpoints_7491  s     Zq!Z1%Z#Z1%\8S)\63'\63') >====>>>>>!#w///@@4@@@FFFFF!#w/////r2   c                     d\  }}t          j        ||                                           \  }}d\  }}t          ||           t          ||           d S )N)rV  r   )g4U?g&MI?)r6   rM	  r   )rp   r  r0	  r|  variancemean_hcvariance_hcs          r0   test_burr_stats_9544zTestBurr.test_burr_stats_9544  s_    1Aq))//11h  Gg&&&+.....r2   c                    d\  }}t          j        ||                                           \  }}t          t          j        |                     t          t          j        |                     d\  }}t          j        ||                                           \  }}t          t          j        |                     t          t          j        |                     d\  }}t           j                            t          j        g d          ||          \  }}}}t          t          j        |                     t          t          j        |                     t          t          j        |                     t          t          j        |                     d\  }}t           j                            g d||          \  }}}}t          t          j        |                     t          t          j        |                     t          t          j        |                     t          t          j        |                     d\  }}t           j                            g d||          \  }}}}t          t          j        |                     t          t          j        |                     t          t          j        |                     t          t          j        |                     d\  }}t           j                            g d||          \  }}}}t          t          j        |                     t          t          j        |                     t          t          j        |                     t          t          j        |                     d\  }}t           j                            g d||          \  }}}}t          t          j        |                     t          t          j        |                     t          t          j        |                     t          t          j        |                     d S )N)ry   r   )r  r   )r   rd   r   r   )r  r   )r  r   )r  r   )r6   rM	  r	   rg   rw  r  _munpr   )	rp   r  r0	  r|  rZ	  e1e2e3e4s	            r0   test_burr_nan_mean_var_9544z$TestBurr.test_burr_nan_mean_var_9544  sb   1Aq))//11h""###1Aq))//11hD!!"""""###1))"(<<<*@*@!QGGBB1)),,,1==BBB   1)),,,1==BBB   B   1)),,,1==BBB   B   B   1)),,,1==BBB   B   B   B     r2   N)r   r   r   rX	  r]	  rd	  r8   r2   r0   rP	  rP	    sA        0 0 0(	/ 	/ 	/(! (! (! (! (!r2   rP	  c                   Z    e Zd Zej                            dddg          d             ZdS )
TestBurr12zscale, expected)rU  gd~)r  gR톇T c                 r    t           j                            dddd|          }t          ||d           d S )Ng     jAg     jAr   r?  r  r   r   )r6   rW	  r/  r   )rp   rc   rU   r  s       r0   r0  zTestBurr12.test_delta_cdf  s?    ( ''S!Qe'DDxe444444r2   N)r   r   r   r   r   r   r0  r8   r2   r0   rf	  rf	    sP        [.<;=> >5 5> >5 5 5r2   rf	  c            	       x   e Zd Zg dZg dZg dZ ej        eeef          Zg dZ	ddddd	ej
        gZg d
Z e e ee	ee          e                    Zddddej
        dfddej
        dfddej
        dfgZd Zej        j        d             Zej                            e          ZdZ eej                            ee                    5 Z e j!        e          Z"ddd           n# 1 swxY w Y   ej        #                    de"d                   d             Z$ej        #                    de"d                   d             Z%ej        j        ej        &                    d          ej        #                    de"d                   d                                     Z'd Z(ej        j)        d             Z*ej        #                    de          d              Z+ej        j        ej        &                    d          d!                         Z,ej        j)        d"             Z-d# Z.d$ Z/d% Z0dS )&TestStudentizedRange)gQ1@g33333F@g
ףp=*K@gHzM@g/$@g~j!@g33333$@g{Gz&@gh|?5	@gQ8@g&1@g|?5@g@gOn@g!rhm@gB`"@r  gʡEs@g|?5^@g/$@gV-@g/$@gF@g?5^I@)gRV@gffffffl@gp@g     r@gʡ @gHzG/@gQ82@gQ3@g!rh@g     @g+@gʡEs @gjt@gB`"[@g@gnJ@gV-@gFx@gsh|?@g+N@g/$@g @g@gGz@)gfffff"@i  i
  i  gHzG2@g(\A@gQC@gfffffE@g @gNbX9"@gHz$@g(\&@g-@gn@@gw/@g=
ףp @gJ+@g-'@gn@gHz@gV-@gnJ@g$@g/ݤ@)r  r%  r  r   r   r]   r  x   )rd   r?  r  r  )rZ   r   i)#  gupm1f?)r   r]   r   g?<-=A?gv"?r   gd暕?ga-A?c                     | j         D ]>\  }}|\  }}}t          j                            |||          }t	          ||d           ?d S )Nr  r   )r   r6   studentized_rangern   r   )rp   pvkr  
p_expectedrA  rY   res_ps          r0   test_cdf_against_tablesz,TestStudentizedRange.test_cdf_against_tables&  s_    i 	: 	:FC"J1+//1a88EE:D99999	: 	:r2   c                     | j         D ]>\  }}|\  }}}t          j                            |||          }t	          ||d           ?d S )NMb@?r   )r   r6   rl	  r  r   )rp   rm	  
q_expectedrw  rA  rY   res_qs          r0   test_ppf_against_tablesz,TestStudentizedRange.test_ppf_against_tables,  s^    #y 	: 	:OCGAq!+//1a88EE:D99999	: 	:r2   z&data/studentized_range_mpmath_ref.jsonNcase_resultcdf_datac                     |d         }|d         }|d         |d         |d         f}t          j        j        | }t          |||d         |d                    d S 	Nsrc_case	mp_resultr  rY   rA  expected_atolexpected_rtolr   )r6   rl	  rn   r   rp   rv	  rz	  r{	  qkvr   s         r0   test_cdf_against_mpz(TestStudentizedRange.test_cdf_against_mp8  s    z*,	smXc]HSM9%)3/Y%o6%o6	8 	8 	8 	8 	8 	8r2   pdf_datac                     |d         }|d         }|d         |d         |d         f}t          j        j        | }t          |||d         |d                    d S ry	  )r6   rl	  rf   r   r~	  s         r0   test_pdf_against_mpz(TestStudentizedRange.test_pdf_against_mpC  r	  r2   z+intermittent RuntimeWarning: invalid value.moment_datac                    |d         }|d         }|d         |d         |d         f}t          j        d          5  t          j        j        | }d d d            n# 1 swxY w Y   t          |||d         |d	         
           d S )Nrz	  r{	  r@  rY   rA  r5  r6  r|	  r}	  r   )rg   rD  r6   rl	  r  r   )rp   rv	  rz	  r{	  mkvr   s         r0   test_moment_against_mpz+TestStudentizedRange.test_moment_against_mpN  s     z*,	smXc]HSM9 [*** 	7 	7)0#6C	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	Y%o6%o6	8 	8 	8 	8 	8 	8s   AA!$A!c                     d\  }}t          t          j        j        dt          j        ||f          }t          |d         d           d S )Nr   r]   r   r  r   )r   r6   rl	  rf   rg   r  r   )rp   rY   rA  r   s       r0   test_pdf_integrationz)TestStudentizedRange.test_pdf_integration_  sG    15*.26AGGGA"""""r2   c                    d\  }}t          j        ddd          }t          j                            |||          dd          }t          j                            |||          }t          ||          }t          ||d           d S )	Nr	  r   r]   r{   )stepr   r  r   )rg   r  r6   rl	  rn   rf   r   r   )rp   rY   rA  r\   y_cdf	y_pdf_rawy_pdf_cumulatives          r0   test_pdf_against_cdfz)TestStudentizedRange.test_pdf_against_cdfe  s    1
 Ia$''''++Aq!44QRR8+//1a88	/	1== 	(%d;;;;;;r2   r_case_resultc                     |\  }}}}t          j        d          5  t          j                            |||          }d d d            n# 1 swxY w Y   t          ||           d S )Nr5  r6  )rg   rD  r6   rl	  rn   r   )rp   r	  r  rY   rA  r_resr   s          r0   test_cdf_against_rz'TestStudentizedRange.test_cdf_against_ru  s     '1a[*** 	7 	7)--aA66C	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7U#####s   "AAAc                    t          j        d          5  t          j                            ddgddgddg          }d d d            n# 1 swxY w Y   t          |j        d	           t          j        t          d
          5  t          j                            dddgg d           d d d            d S # 1 swxY w Y   d S )Nr5  r6  r   rd   r   r   r]   r  r  z...could not be broadcast...r  )r]   r  rW  )
rg   rD  r6   rl	  r_	  r   rC  r   r   r  r  s     r0   test_moment_vectorizationz.TestStudentizedRange.test_moment_vectorization}  sh    [*** 	H 	H'--q!fq!fr2hGGA	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	&&&]:-KLLL 	C 	C#))!aV\\\BBB	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	Cs#   (A

AA&B88B<?B<c                    t                      5 }t          j        d          5  |                    t                     t
          j                            g d          \  }}}}d d d            n# 1 swxY w Y   d d d            n# 1 swxY w Y   t          t
          j        	                    ||                     d S )Nr5  r6  r	  )
r   rg   rD  rP   r   r6   rl	  r  r	   	_argcheck)rp   r~  rY   r  r   s        r0   test_fitstart_validz(TestStudentizedRange.test_fitstart_valid  sF      	GCX)F)F)F 	G 	GJJ)***1;;IIIFFKAr1a	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	'11!R8899999s5   B	AA2&B	2A6	6B	9A6	:B		BBc                    t           j                            ddt          j                  }t           j                            ddd          }t          ||dd           t           j                            ddt          j                  }t           j                            ddd          }t          ||dd           d S )Nr   r]   韆 r  r   )r6   rl	  rf   rg   r  r   rn   )rp   r   
res_finites      r0   test_infinite_dfz%TestStudentizedRange.test_infinite_df  s     %))!R88,00B>>
Zd>>>>%))!R88,00B>>
Zd>>>>>>r2   c                 Z   t           j                            ddd          }t           j                            ddd          }t           j                            ddd          }t          t          t
          ||dd           t          ||dd           t           j                            ddd          }t           j                            ddd          }t           j                            ddd          }t          t          t
          ||dd           t          ||dd           d S )Nr   r]   r   r	  i r  r   )r6   rl	  rf   r?  AssertionErrorr   rn   )rp   r   r	  
res_sanitys       r0   test_df_cutoffz#TestStudentizedRange.test_df_cutoff  s    %))!R88,00B>>
,00B>>
nosJd	, 	, 	, 	,
JTEEEE%))!R88,00B>>
,00B>>
nosJd	, 	, 	, 	,
JTEEEEEEr2   c                     d\  }}}t           j                            |||          }t          |dd           |dk    sJ d S )N)gaRA@r   iS  r   r  r   )r6   rl	  r  r   )rp   r  rY   rA  rw  s        r0   test_clippingz"TestStudentizedRange.test_clipping  sO     .1a#&&q!Q//15))))Avvvvvvr2   )1r   r   r   q05q01q001rg   r  qspsr  vskslistr  r%   r   r_datarp	  r   r   r  ru	  ospathdirnamer  path_prefixrelative_pathopenrs  filejsonr  pregenerated_datar   r	  r	  xfail_on_32bitr	  r	  r   r	  r	  r	  r	  r	  r	  r	  r8   r2   r0   ri	  ri	    sv       ' ' 'C' ' 'C( ( (D 
c4(	)	)B			B
QBRV	$B	B4GGBB'',,--D
 	*(	
Arv()	
Arv()	
B)*F: : : [: : : '//(++K<M	bgll;66	7	7 ,4%DIdOO, , , , , , , , , , , , , , , [],=j,IJJ8 8 KJ8 [],=j,IJJ8 8 KJ8 [[ MNN[],=m,LMM8 8 NM ON 8# # # [< < < [_f55$ $ 65$ [[ MNNC C ON C [: : :	? 	? 	?F F F*    s   C00C47C4ri	  c                  ,   t          t          j                            d          ddd           t          t          j                            d          ddd           t          t          j                            dd	d
          ddd           d S )Ng2g?r]   test_540_567)rY  rm  g2gk?g;B.?gͣh?gHŎ*?ra   g.y?)r   r6   r  rn   r8   r2   r0   r	  r	    s    
}557J "N< < < <
}557K "N< < < <
}.-; ' = =+ "N< < < < < <r2   c                  d    t          t          j                            dd          dd           d S )Nr~   rd   ry   r  r  r8   r2   r0   test_regression_ticket_1326r	    s*    
sA..R88888r2   c            	         t          j        ddd          } t          j        d          5  dddt          j        dgdgdgg          fD ]{}t          j                            | |          }t          |dk                                               t          t          j	        |                                                      |t          j        dgdgd	gg          }t          j                            | |          }d d d            n# 1 swxY w Y   t          t          j	        |                                                      t          |d
         dk                                               t          |d         dk                                               t          |d         dk    
                                           t          |d         dk    
                                           d S )N      rV  r[   r5  r  r~   r  rI  r}   r   r   rd   )rg   rZ  rD  r   r6   r(   rf   r	   rB  rw  any)r\   r=  rw  s      r0   test_regression_tukey_lambdar	    s    	D#s##A	H	%	%	% * *tRXvutf.E%F%FG 	( 	(C!%%a--AQ#XNN$$%%%RXa[[__&&&''''hu-..!!!S))* * * * * * * * * * * * * * * RXa[[__QqTS[   QqTS[   QqTS[   QqTS[     s   CDDDzdocstrings strippedr  c                      t          dt          j        j        v           t          dt          j        j        v            d S )Nzpdf(x, mu, loc=0, scale=1)zpmf(x,)r	   r6   r  r7  r8   r2   r0   test_regression_ticket_1421r	    s9    (0EEFFFH--.....r2   c            	      	   t          j        d          5  t          t          j        t          j                            dt           j                                       t          t          j        t          j                            dt           j                                       t          t          j        t          j        	                    dt           j                                       t          t          j        t          j        
                    dt           j                                       t          t          j        t          j                            dt           j                                       t          t          j        t          j                            dt           j                                       t          t          j        t          j                            dt           j                                       t          t          j        t          j                            dt           j                                       t          t          j        t          j                            t           j        d                               t          t          j        t          j                            t           j        d                               t          t          j        t          j        	                    t           j        d                               t          t          j        t          j        
                    t           j        d                               t          t          j        t          j                            t           j        d                               t          t          j        t          j                            t           j        d                               t          t          j        t          j                            t           j        d                               t          t          j        t          j                            t           j        d                               d d d            d S # 1 swxY w Y   d S )Nr5  r6  r   ry   )rg   rD  r	   rw  r6   r+  r  r  rn   rw  r  rf   r   r  r  r  rQ  r  r8   r2   r0    test_nan_arguments_gh_issue_1362r	    s)   	X	&	&	& < <262233444Q//00111q"&1122333Arv..//000Q//00111262233444Q//00111Q//00111//<<==>>>,,RVS99::;;;..rvs;;<<===++BFC8899:::,,RVS99::;;;//<<==>>>,,RVS99::;;;,,RVS99::;;;#< < < < < < < < < < < < < < < < < <s   RR44R8;R8c                     t           j                            d           t          j        g d          } t          j                            | d         | d         | d         d          }t          j        d	          5  t          j        t          j                            |d
                    }d d d            n# 1 swxY w Y   t          || d           t          j        t          j                            |dd                    }t          || d           t          j        t          j                            |dd                    }t          || d           t          j        t          j                            |dd                    }t          || d           t           j                            d           d}d}t          j
                            |dd          }t          j        t          j
                            ||                    }t          j        |t          j        ||z
  dz                                            g          }t          ||d           d S )Ni.  )r   r~   ry   r   r   rd   r^   r:  r5  r	  r~   r   rX  ry   )r   rb   r   )r   rb   r  r  r}   r   )rg   r   r   r   r6   r&  r   rD  r   r   r  r)  r|  )truer\   r  rb   r   rU   s         r0   test_frozen_fit_ticket_1536r	     sL   INN48OOO$$D$q'47DG#>>A	H	%	%	% 9 9%-++AB+77889 9 9 9 9 9 9 9 9 9 9 9 9 9 9 a0000Xem''#1'==>>Fa0000Xem''d'::;;Fa0000Xem''d';;<<Fa0000INN4
CD
sBS))AXejnnQTn2233Fxrw4!'9'9';';<<=>>H!444444s    4C  CCc                      t           j                            d           t          j                            d          } t          j                            |           }d}t          ||d           d S )Ni	 r^   r:  )g
ףp=
?gʡE?r   rX  )rg   r   r   r6   r.  r   r   r   )r   r  rU   s      r0   test_regression_ticket_1530r	    sc    INN6
,



$
$C\c""FH!444444r2   c                     t           j                            d           t           j                            d          } dD ]K}t          j                            | |z             \  }}t          ||d           t          |dd           Ld S )Nr4  r  )r  g   6ArU  r   r  )rg   r   r   r  r6   r.  r   r   )r\   offsetrb   rc   s       r0   test_gh_pr_4806r	  %  s    INN4
	A' . .\%%a&j11
UV#....s-----. .r2   c                  t   t           j                             dd          } dt          j        dz  dz  ddg}t	          | |d           t           j                             d	d          } g d
}t	          | |d           t           j                             dd          } g d}t	          | |d           d S )Nr   rW  rX  rd   r   r  r]   rX  g
ףp=
	@)r   gz5v?r   gRTgQ?)r   gNg @r   gJFٻ)r6   r(   rg   rh   r   )rD  rU   s     r0   "test_tukeylambda_stats_ticket_1545r	  /  s     
		 	 F	 	3	3B25!8A:q#&HHb1111			 	 v	 	6	6BCCCHHb1111			 	 v	 	6	6BCCCHHb111111r2   c                      t          t          j        t          j                            dd                               d S )Nr  r  )r	   rg   r  r6   r  r  r8   r2   r0   test_poisson_logpmf_ticket_1436r	  C  s2    BK,,T3778899999r2   c                      ddg} | D ]6\  }}t           j                             |d          }t          ||           7dS )a  Test the powerlaw stats function.

    This unit test is also a regression test for ticket 1548.

    The exact values are:
    mean:
        mu = a / (a + 1)
    variance:
        sigma**2 = a / ((a + 2) * (a + 1) ** 2)
    skewness:
        One formula (see https://en.wikipedia.org/wiki/Skewness) is
            gamma_1 = (E[X**3] - 3*mu*E[X**2] + 2*mu**3) / sigma**3
        A short calculation shows that E[X**k] is a / (a + k), so gamma_1
        can be implemented as
            n = a/(a+3) - 3*(a/(a+1))*a/(a+2) + 2*(a/(a+1))**3
            d = sqrt(a/((a+2)*(a+1)**2)) ** 3
            gamma_1 = n/d
        Either by simplifying, or by a direct calculation of mu_3 / sigma**3,
        one gets the more concise formula:
            gamma_1 = -2.0 * ((a - 1) / (a + 3)) * sqrt((a + 2) / a)
    kurtosis: (See https://en.wikipedia.org/wiki/Kurtosis)
        The excess kurtosis is
            gamma_2 = mu_4 / sigma**4 - 3
        A bit of calculus and algebra (sympy helps) shows that
            mu_4 = 3*a*(3*a**2 - a + 2) / ((a+1)**4 * (a+2) * (a+3) * (a+4))
        so
            gamma_2 = 3*(3*a**2 - a + 2) * (a+2) / (a*(a+3)*(a+4)) - 3
        which can be rearranged to
            gamma_2 = 6 * (a**3 - a**2 - 6*a + 2) / (a*(a+3)*(a+4))
    )rU  )ry   ru  r~   rv  )r}   )gUUUUUU?r(  g^cQg333333rW  rX  N)r6   r3  r   )r  r.   
exact_mvskrW  s       r0   test_powerlaw_statsr	  G  s[    > ,=?E 4 4:~##Av#66!$
33334 4r2   c                  f    t           j                            dd          } t          | d           d S )Nr   r   r~   )r6   r3  r   r   rw  s    r0   test_powerlaw_edger	  m  s/    a##ACr2   c                  x   t           j                            dd          } t          | d           t           j                            dg d          } t          | t
          j        ddg           t           j                            dg d          } t          | t
          j        dt
          j         g           d S )Nr   r   r~   )r   rU  r  rU  )r6   rj  r   r   rf   rg   r  r	  s    r0   test_exponpow_edger	  s  s    a##AC 	1...//ARVS#&'''a!1!1!122ARVS26'*+++++r2   c                  h    t           j                            ddd          } t          | d           d S )Nr   r   rU  )r6   gengammarf   r   r	  s    r0   test_gengamma_edger	    s1    1a##ACr2   za, c, ref, tol))g    `6Ar   g2j!@r   )r  r   ggA@r   )r  r   r  r   )r  r   g #@r   )g    `FAr  gI~mr   )gl$W}Lr  g.I#Ur   c                 f    t          t          j                            | |          ||           d S rL  )r   r6   r	  rE   )r.   r  r  r   s       r0   test_gengamma_extreme_entropyr	    s1    " EN**1a00#C@@@@@@r2   c                      t           j                            ddd          } | dk    sJ t           j                            ddd          }|t          j         k    sJ d S )Nr   r   r   r~   )r6   r	  rf   r   rg   r  )rw  r[  s     r0   !test_gengamma_endpoint_with_neg_cr	    sV    1a$$A8888>  Ar**DBF7??????r2   c                      t           j                            ddd          } t          | d           t           j                            ddd          } t          | d           d S )Nr   r  rU  g>r]   gqq?)r6   r	  r_	  r   r	  s    r0   test_gengamma_munpr	    sZ    Rb))A:&&&RR((A6"""""r2   c                     t          j        g d          } t          j        d          5  t                      5 }|                    t
          d           |                    t          d           t          j        	                    |            d d d            n# 1 swxY w Y   d d d            d S # 1 swxY w Y   d S )N)0g>X*ȿgPix#?g=?g&^?goϿg뵏˿gO_ZQ?g\?g~?g)/?gRܶ?g핚οgH߃[g?gS"gm_ пg7k?g#BF?gKU=?gT?gZg[Qs?g2?g6Hwƭ8?g*-
?ga]?g'?g޻?g?J_ ?g~sw?g0FfͿgg"@ӿg?%:˿g&zM?g?Gg	F?g~,g HgW2ҿgTzy?gwmǿg @gW=ֿg	't?g".v1glg.Hꮿg,?g*˿r5  r6  z:The maximum number of subdivisions .50. has been achieved.z-floating point number truncated to an integer)
rg   r   rD  r   rP   r   r{  r6   r  r   )r0	  r~  s     r0   test_ksone_fit_freezer	    sK   
		/ 		/ 		/
	0 
	0A 
X	&	&	&     	CJJ)#$ $ $ JJ~FH H HKOOA	 	 	 	 	 	 	 	 	 	 	 	 	 	 	                 s5   B5ABB5B!	!B5$B!	%B55B9<B9c            	      r   t          j        t          t          ddd                               } g d}t	          t          j                                        |           |d           t	          t          j                                        | dz             j        |d           t
          j                            | dz             d	z  j	        }t          j
        t
          j                            |           t
          j                            |           z
            }t	          ||d	           d S )
Nr   rj	  r   )gDB.g8_$g%`OAgjhwHRgWMB@v`g7VY}igۦx\Arg	xg#g/dg3$gegd)gNq{3gيGǓgr4g37'
gfFg?dJgضg2,
gm%gӅJgz;pgɿ{gk2gij<%giVSͶgBR4g
Q/Mr  r   y        +=y        |=r  )rg   r   r	  r   r   r6   r  r  realimagr   r   )r\   rU   derivderiv_expecteds       r0   test_norm_logcdfr	    s
    
Dq#q))**	+	++A0 0 0H EJLL''**H4@@@@ EJLL''F
338(NNNN Zq6z**506EVEJ--a005:3D3DQ3G3GGHHNE>666666r2   c                  "   t          j        g d          } t          j        g d          }t          j                            |           }t          ||d           t          j                            |          }t          || d           d S )N)r   rU  ry   rZ   r{   r_  )g~V1?r  gba"?g܄4ťY?r  g$%+Ir  r   r   )rg   r   r6   r$  rn   r   r  )r\   rU   r  r  s       r0   test_levy_cdf_ppfr	    s    
33344A x 1 1 1 2 2H 	
qAAxe,,,, 
	!	!BB&&&&&&r2   c                      t          j        g d          } t          j        g d          }t          j                            |           }t          ||d           d S )N)r  rG  gMraB3Gr  )gep[>g}XEQ=gѭEG<g?_%~:r~  r   )rg   r   r6   r$  r  r   r\   rU   r  s      r0   test_levy_sfr	    sh    
)))**Ax 0 0 0 1 1H 	
aAAxe,,,,,,r2   zp, expected_isf))r}  gj1e2H)r  g6C)r  gnE@)rr  g!^x1?)r  gZ?)g   ?g:}!Nu?c                 h    t           j                            |           }t          ||d           d S )Nr`  r   )r6   r$  r  r   )rw  expected_isfr\   s      r0   test_levy_isfr	  	  s2     	
qAA|%000000r2   c                      t          j        g d          } t          j        g d          }t          j                            |           }t          ||d           d S )N)gMb{Gzg{Gztg~jtX)g#]<gOul2;gޢا6g̅7=!r   r   )rg   r   r6   r%  r  r   r	  s      r0   test_levy_l_sfr	    sh    
11122Ax 1 1 1 2 2H 	AAxe,,,,,,r2   c                      t          j        g d          } t          j                            |           }t          j                            |          }t          || d           d S )N)g [n<r   r%  r  r   )rg   r   r6   r%  r  r  r   )rw  r\   r  s      r0   test_levy_l_isfr	  !  s[    
&&&''AAAAqu%%%%%%r2   c                     t          t          j                            dddd          d           t          t          j                            dddd          d           t          t          j                            dddd          d           t          t          j                            d	d
d
d          d           t          t          j                            dd
d
d          d           d S )Nr  i i  i  )g      c@g     h@g=
ףp=?Gz?)g      c@g     h@ri  r^   r?  r   )r   r6   rp  r  r  r8   r2   r0   test_hypergeom_interval_1802r	  )  s    ))#vucBB! ! !))$sCC! ! ! ))#vucBB! ! ! $$T3Q77;;;$$QS!44a88888r2   c                     t           j                            d           t          j        ddd          } t	          t
          t          j        j        | ddd	           t	          t
          t          j        j        | ddd
d	           t	          t
          t          j        j        | ddd
d           t	          t
          t          j        j        | dddd           t	          t
          t          j        j	        dddd           t	          t
          t          j        j
        | dddd           t	          t
          t          j        j        | dddd           t	          t
          t          j        j        dddd           t	          t
          t          j        j        dddd           t	          t
          t          j        j        | dddd           t          j                            | dd           t          j                            | ddd
           t          j                            dd           t          j                            ddd
           t          j                            ddd
d           t          j        	                    ddd
d           t          j                            t          j        	                    dd          d           t          j                            | dd	           t	          t
          t          j        j        | ddd
           t	          t
          t          j        j        | ddd
	           t	          t
          t          j        j        | dd	           t	          t
          t          j        j        | dd
dd	           t	          t
          t          j        j        | dd
ddd           t	          t
          t          j        j        | dd
ddd	           t	          t
          t          j        j        | dd
dddd	  	         t          j                            | dd
ddd           d S )Nr4  rZ   r  r   numrd   r   rU  r.  r   ry   ra   r}   rD  r  r:  r  r  )rg   r   r   rZ  r?  r  r6   rZ  rf   r   rn   r  rE   r   re  rQ  r  r  r  r   s    r0   test_distribution_too_many_argsr	  8  sX   INN4 	C!$$$A)U[_aA3????)U[_aAqcBBBB)U[_aAq!<<<)U[_aA3cJJJJ)U[_b!CHHHH)U[_aQCsKKKK)U[_aQCsKKKK)U[.A3cJJJJ)U[0"aSLLLL)U[_aQCsKKKK 
KOOAq!	KOOAq!Q	Kb!	Kb!Q	Kb!Q%%%	KOOB1a   	KOOEKOOBQO//444 
JNN1aQN)UZ^Q1a888)UZ^Q1!<<<< )U[_a<<<<)U_0!Q1#FFFF)U_0!Q1c3GGG)UY]Aq!QsCCCC)UY]Aq!Q3cJJJJ	IMM!Q1a%%%%%r2   c                      t           j                            t          j        ddd          dd          } t           j                            t          j        ddd          dd          }t          | |dd           d S )	Nr  r  r  rd   gYZ@r_  r   rh  )r6   ncx2rn   rg   r  _cdfvecr   r@  s     r0   test_ncx2_tails_ticket_955r
  `  sm     	
ryR--q.AAA
29RS111nEEAAqt!,,,,,,r2   c            
      *   t          j                    5  t          j        dt                     t	          t
          j                            dt          j	        dd          d          d           t
          j        
                    dt          j	        dd          d          } d d d            n# 1 swxY w Y   t          t          j        |                                                      t          j                    5  t          j        dt                     t	          t
          j                            ddd	          d           t          t
          j        
                    ddd	          d
           d d d            d S # 1 swxY w Y   d S )Nrt  r   iT  i^  rd   r   r  r   rW  gsq6)rx  ry  rz  r{  r   r6   r	  rf   rg   r  r   r	   rW  rB  r   )logvals    r0   test_ncx2_tails_pdfr
  h  s    
	 	"	" > >g~666UZ^^Aryc':':A>>BBB""1biS&9&91==> > > > > > > > > > > > > > >
 BK##%%&&& 
	 	"	" M Mg~666UZ^^E1b111555
))%B779KLLLM M M M M M M M M M M M M M M M M Ms%   BB11B58B5A9FFFzmethod, expectedrn   gu%>g	;Q=rf   g<x>gRz\R>r   gʎK$/gԆX1r  gfHu@ge:@c                 z     t          t          j        |           dddgd          }t          ||d           d S )NrZ   r   r   r]   )r  r  r   r   )r,  r6   r	  r   )r  rU   r  s      r0   test_ncx2_zero_ncr
  y  sE      )WUZ((!QB???FFH5111111r2   c                      t           j                            ddd          } t           j                            dd          }t	          | |d           d S )Nr]   r   r   )r  r  r   )r  r   r   r   )r6   r	  r   r  r   )r  rU   s     r0   test_ncx2_zero_nc_rvsr
    sO     Z^^raa^88Fz~~!~44HFH5111111r2   c                      dt          j        dd          z  } t          t          j                            dd|           d           d S )Nr]   r   r  r   r  r  r   )rg   r  r   r6   r	  rn   )r  s    r0   test_ncx2_gh12731r
    sB    	RYq"	Bb11155555r2   c                      t          j        g d          } d\  }}t          j                            | ||          }g d}t          ||d           d S )N)gю]	@gj%@gb	y/7@g H@gIZ@gXl@g'/2?8@gݰmА@gU@gy]`'@g@g*\@g48c@)r  gh ?8@r

  )rU  rU  rU  rU  rU  g?gy[qD?r~   r~   r~   r~   r~   r~   r  r   )rg   r   r6   r	  r  r   )r\   nur=  r  sf_expecteds        r0   test_ncx2_gh8665r
    st    
 " " " 	# 	#A
 %GB	qRC	(	(B' ' 'K
 B%000000r2   c            	         d} d}t          j        t          j                            d| |          t          j                            d| |          d          }t          j                            || |          }t          j                            || |z   t          j        d| z  d|z  z                       }t          ||d	
           d S )Ni,  i  r_  r  r  r	  rd   r   r  r   )	rg   rZ  r6   r	  r  rf   r  r)  r   )r  r  r\   ncx2_pdfgauss_approxs        r0   test_ncx2_gh11777r
    s    
 
B	B
EJNN5"b11JNN5"b11u	> 	> 	>Az~~aR((H:>>!R"Wbga"fq2vo.F.FGGLHl666666r2   zx, c, expected))rd   r   g|1q?)rd   rd   g~?)r  r   V<3T1=) 7yQCr   u	lY<)r  g   vHGBg^b!*1=)r
  r  gS?c                 h    t           j                            | |          }t          ||d           d S Nr  )r6   
foldcauchyr  r   r\   r  rU   r  s       r0   test_foldcauchy_sfr
    s4     
			Q	"	"BB%(((((r2   rX  ))rd   g?)r  r
  )r
  r
  )g6ްPg8R#/c                 f    t           j                            |           }t          ||d           d S r
  )r6   
halfcauchyr  r   )r\   rU   r  s      r0   test_halfcauchy_sfr
    s2     
			Q		BB%(((((r2   zp, expected))g?g*wӄZ>)333333?gN9?)ry   rU  )r{   g8<,O@)r~  g:B)gl ׶w/gMb}[Pc                 d    t           j                            |           }t          ||           d S rs   )r6   r
  r  r   )rw  rU   r\   s      r0   test_halfcauchy_isfr!
    s0     	QAAx     r2   c                  x    t          j        dd          } t          |                     d          d           d S )Nr   r   r  )r6   r  r   rn   )rQ  s    r0   test_foldnorm_zeror#
    s6    		#	#	#BAr2   ))rd   r   gwo{?)r  r   gGd-P/)r]   r>  gof?)r  r>  gOul";c                 h    t           j                            | |          }t          ||d           d S )Nr~  )r6   r  r  r   r
  s       r0   test_foldnorm_sfr%
    s3     
		1a	 	 BB%(((((r2   c                     t           j                             g ddd          } t           j                             ddgdd          }t          d |D                       }t          ||            t           j                             g d          } t           j                             ddg          }t          d	 |D                       }t          ||            d S )
N)r~   ry   rU  r   ry   rU  c              3   R   K   | ]"}t           j        t           j        |f         V  #d S rs   rg   rO  r  rb  s     r0   r  z-test_stats_shapes_argcheck.<locals>.<genexpr>  s/      88q"%	*888888r2   )rd   r  r   rd   r  c              3   R   K   | ]"}t           j        |t           j        f         V  #d S rs   r(
  rb  s     r0   r  z-test_stats_shapes_argcheck.<locals>.<genexpr>"  s/      88q"%26	*888888r2   )r6   r   tupler   r&  )mv3mv2mv2_augmenteds      r0   test_stats_shapes_argcheckr.
    s     .

3
7
7C
.

Sz1c
2
2C88C88888M$$$ -

lll
+
+C
-

q#h
'
'C88C88888M$$$$$r2   c                       e Zd Zd ZdS )
_distr_genc                     dS Nr  r8   rp   r\   r.   s      r0   _pdfz_distr_gen._pdf-  s    rr2   Nr   r   r   r4
  r8   r2   r0   r0
  r0
  ,  s#            r2   r0
  c                       e Zd Zd ZdS )_distr2_genc                     d|z  |z   S r2
  r8   r3
  s      r0   _cdfz_distr2_gen._cdf2      Avzr2   N)r   r   r   r9
  r8   r2   r0   r7
  r7
  1  s#            r2   r7
  c                       e Zd Zd Zd ZdS )_distr3_genc                     ||z   S rs   r8   rp   r\   r.   r/   s       r0   r4
  z_distr3_gen._pdf7  s    1ur2   c                     d|z  |z   S r2
  r8   r3
  s      r0   r9
  z_distr3_gen._cdf:  s     Avzr2   Nr   r   r   r4
  r9
  r8   r2   r0   r<
  r<
  6  s2              r2   r<
  c                       e Zd Zd Zd ZdS )_distr6_genc                     ||z  |z   S rs   r8   r>
  s       r0   r4
  z_distr6_gen._pdfB  s    sQwr2   c                     d|z  |z   S r2
  r8   r>
  s       r0   r9
  z_distr6_gen._cdfE  r:
  r2   Nr@
  r8   r2   r0   rB
  rB
  @  s2              r2   rB
  c                   t    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd Zd Zd Zd Zd Zd ZdS )TestSubclassingExplicitShapesc                 r    t          dd          }t          |                    dd          d           d S )Ndummyr.   r  r  r   r  r  r0
  r   rf   rp   dummy_distrs     r0   test_correct_shapesz1TestSubclassingExplicitShapes.test_correct_shapesL  s:     gc:::[__Q!_,,b11111r2   c                 v    t          dd          }t          t          |j        dfi t	          d           d S )NrH
  ArI
  r   r  )r0
  r?  r  rf   r  rK
  s     r0   test_wrong_shapes_1z1TestSubclassingExplicitShapes.test_wrong_shapes_1P  s>     gc:::i!AAtayyyAAAAAr2   c                 ~    t          dd          }t          ddd          }t          t          |j        dfi | d S )NrH
  za, b, crI
  r   rd   r   r  )r0
  r  r?  r  rf   )rp   rL
  r-  s      r0   test_wrong_shapes_2z1TestSubclassingExplicitShapes.test_wrong_shapes_2T  sJ     gi@@@Q!q!!!i!;;s;;;;;r2   c                 X    t          dd          }t          t          t          fi | d S )NrH
  r  rI
  )r  r?  r  r0
  rp   r-  s     r0   test_shapes_stringz0TestSubclassingExplicitShapes.test_shapes_stringY  s2    +++i33s33333r2   c                 X    t          dd          }t          t          t          fi | d S )NrH
  z(!)rI
  r  r?  SyntaxErrorr0
  rT
  s     r0   test_shapes_identifiers_1z7TestSubclassingExplicitShapes.test_shapes_identifiers_1^  s2    ...k:5555555r2   c                 X    t          dd          }t          t          t          fi | d S )NrH
  4chanrI
  rW
  rT
  s     r0   test_shapes_identifiers_2z7TestSubclassingExplicitShapes.test_shapes_identifiers_2c  2    000k:5555555r2   c                 X    t          dd          }t          t          t          fi | d S )NrH
  zm(fti)rI
  rW
  rT
  s     r0   test_shapes_identifiers_3z7TestSubclassingExplicitShapes.test_shapes_identifiers_3g  s2    111k:5555555r2   c                 X    t          dd          }t          t          t          fi | d S )NrH
  za=2rI
  rW
  rT
  s     r0   "test_shapes_identifiers_nodefaultsz@TestSubclassingExplicitShapes.test_shapes_identifiers_nodefaultsk  s2    ...k:5555555r2   c                 X    t          dd          }t          t          t          fi | d S )NrH
  z*argsrI
  rW
  rT
  s     r0   test_shapes_argsz.TestSubclassingExplicitShapes.test_shapes_argso  r]
  r2   c                 X    t          dd          }t          t          t          fi | d S )NrH
  z**kwargsrI
  rW
  rT
  s     r0   test_shapes_kwargsz0TestSubclassingExplicitShapes.test_shapes_kwargss  s2    
333k:5555555r2   c                 X    t          dd          }t          t          t          fi | d S )NrH
  za, b, c, lambdarI
  rW
  rT
  s     r0   test_shapes_keywordsz2TestSubclassingExplicitShapes.test_shapes_keywordsw  s3    (9:::k:5555555r2   c                      G d dt           j                  } |d          }t          |                    dd          t           j                            d          dz             d S )Nc                       e Zd Zd ZdS )FTestSubclassingExplicitShapes.test_shapes_signature.<locals>._dist_genc                 F    t           j                            |          |z  S rs   r6   r  r4
  r3
  s      r0   r4
  zKTestSubclassingExplicitShapes.test_shapes_signature.<locals>._dist_gen._pdf      zq))A--r2   Nr5
  r8   r2   r0   	_dist_genrj
  ~  #        . . . . .r2   rn
  r.   r  ry   rd   r  r6   rC   r   rf   r  rp   rn
  r?   s      r0   test_shapes_signaturez3TestSubclassingExplicitShapes.test_shapes_signature|  s|    	. 	. 	. 	. 	.+ 	. 	. 	. y$$$TXXcQX'')<)<Q)>?????r2   c                      G d dt           j                  } |d          }t          t          |j        dfi t          dd           d S )	Nc                       e Zd Zd ZdS )STestSubclassingExplicitShapes.test_shapes_signature_inconsistent.<locals>._dist_genc                 F    t           j                            |          |z  S rs   rl
  r3
  s      r0   r4
  zXTestSubclassingExplicitShapes.test_shapes_signature_inconsistent.<locals>._dist_gen._pdf  rm
  r2   Nr5
  r8   r2   r0   rn
  rv
    ro
  r2   rn
  r  rp
  ry   r   rd   r@  )r6   rC   r?  r  rf   r  rr
  s      r0   "test_shapes_signature_inconsistentz@TestSubclassingExplicitShapes.test_shapes_signature_inconsistent  so    	. 	. 	. 	. 	.+ 	. 	. 	. y'''i3AA$a...AAAAAr2   c                     G d dt           j                  } |d          }t          |                    dd          t           j                            d          dz             t          |                    dd          t           j                            d          dz             t          t          |j        dfi t          d           d S )	Nc                       e Zd Zd ZdS )?TestSubclassingExplicitShapes.test_star_args.<locals>._dist_genc                 V    |d         }t           j                            |          |z  S Nr   rl
  )rp   r\   r.  extra_kwargs       r0   r4
  zDTestSubclassingExplicitShapes.test_star_args.<locals>._dist_gen._pdf  s$    "1gzq))K77r2   Nr5
  r8   r2   r0   rn
  r{
    s#        8 8 8 8 8r2   rn
  r~
  rp
  ry   !   r~
  )xxx)r6   rC   r   rf   r  r?  r  r  rr
  s      r0   test_star_argsz,TestSubclassingExplicitShapes.test_star_args  s    	8 	8 	8 	8 	8+ 	8 	8 	8
 y...TXXcrX22EJNN34G4G4JKKKTXXc2&&
s(;(;B(>???i3??$2,,,?????r2   c                 p    G d dt           j                  } |d          }t          |                    ddd          t           j                            d          dz  dz              t          |                    ddd          t           j                            d          dz  dz              d S )	Nc                       e Zd Zd ZdS )ATestSubclassingExplicitShapes.test_star_args_2.<locals>._dist_genc                 \    |d         }t           j                            |          |z  |z   S r}
  rl
  )rp   r\   r	  r.  r~
  s        r0   r4
  zFTestSubclassingExplicitShapes.test_star_args_2.<locals>._dist_gen._pdf  s)    "1gzq))K7&@@r2   Nr5
  r8   r2   r0   rn
  r
    s(        A A A A Ar2   rn
  zoffset, extra_kwargrp
  ry   o   r
  )r	  r~
  rq
  rr
  s      r0   test_star_args_2z.TestSubclassingExplicitShapes.test_star_args_2  s    	A 	A 	A 	A 	A+ 	A 	A 	A
 y 5666TXXc#2X>>Z^^C((+c1	3 	3 	3TXXc3++Z^^C((+c1	3 	3 	3 	3 	3r2   c                      G d dt           j                  } |d          }t          |                    dd          t           j                            d                     d S )Nc                       e Zd Zd ZdS )BTestSubclassingExplicitShapes.test_extra_kwarg.<locals>._distr_genc                 r    |                     dd          }t          j                            |          |z  S )Nr~
  r   )popr6   r  r4
  )rp   r\   r.  kwargsr~
  s        r0   r4
  zGTestSubclassingExplicitShapes.test_extra_kwarg.<locals>._distr_gen._pdf  s0     %jj::zq))K77r2   Nr5
  r8   r2   r0   r0
  r
    s#        8 8 8 8 8r2   r0
  r~
  rp
  r   r   r
  rq
  )rp   r0
  r?   s      r0   test_extra_kwargz.TestSubclassingExplicitShapes.test_extra_kwarg  sw    	8 	8 	8 	8 	8, 	8 	8 	8 z///TXXaQX//1B1BCCCCCr2   c                      G d dt           j                  } |d          }t          |                    d          t           j                            d                     d S )Nc                       e Zd Zd ZdS )ITestSubclassingExplicitShapes.test_shapes_empty_string.<locals>._dist_genc                 @    t           j                            |          S rs   )r6   r  rf   r  s     r0   r4
  zNTestSubclassingExplicitShapes.test_shapes_empty_string.<locals>._dist_gen._pdf  s    z~~a(((r2   Nr5
  r8   r2   r0   rn
  r
    s#        ) ) ) ) )r2   rn
   rp
  ry   rq
  rr
  s      r0   test_shapes_empty_stringz6TestSubclassingExplicitShapes.test_shapes_empty_string  sq    	) 	) 	) 	) 	)+ 	) 	) 	) y###TXXc]]EJNN3$7$788888r2   N)r   r   r   rM
  rP
  rR
  rU
  rY
  r\
  r_
  ra
  rc
  re
  rg
  rs
  rx
  r
  r
  r
  r
  r8   r2   r0   rF
  rF
  I  s"       2 2 2B B B< < <
4 4 4
6 6 6
6 6 66 6 66 6 66 6 66 6 66 6 6
@ @ @B B B@ @ @3 3 3D D D9 9 9 9 9r2   rF
  c                       e Zd Zd Zd Zej                            ed          d             Z	ej                            ed          d             Z
d Zd Zd	 Zd
 ZdS )TestSubclassingNoShapesc                 p    t          d          }t          |                    dd          d           d S )NrH
  r  r   r  r  rJ
  rK
  s     r0   test_only__pdfz&TestSubclassingNoShapes.test_only__pdf  s8     g...[__Q!_,,b11111r2   c                 p    t          d          }t          |                    dd          d           d S )NrH
  r
  r   r  )r7
  r   rf   rK
  s     r0   test_only__cdfz&TestSubclassingNoShapes.test_only__cdf  s8    !w///KOOAO33Q77777r2   docstring strippedr  c                     t          d          }t          |j        d           t          |j        d           t	          j        d|j                  }t          t          |          dk               d S )NrH
  r
  r   r.   zlogpdf\(x, a, loc=0, scale=1\))	r0
  r   numargsr  refindallr7  r	   r  rp   rL
  r   s      r0   test_signature_inspectionz1TestSubclassingNoShapes.test_signature_inspection  sr     !g...[(!,,,['---j:$,. .CAr2   c                     t          d          }t          |j        d           t          |j        d           t	          j        d|j                  }t          t          |          dk               d S )NrH
  r
  rd   r  z!logpdf\(x, a, b, loc=0, scale=1\)r   )	rB
  r   r
  r  r
  r
  r7  r	   r  r
  s      r0   test_signature_inspection_2argsz7TestSubclassingNoShapes.test_signature_inspection_2args  sr     "w///[(!,,,['000j=$,. .CAr2   c                 >    t          t          t          d           d S )NrH
  r
  )r?  r  r<
  ru   s    r0   0test_signature_inspection_2args_incorrect_shapeszHTestSubclassingNoShapes.test_signature_inspection_2args_incorrect_shapes  s    i7;;;;;;r2   c                 x     G d dt           j                  }t          t          |fi t	          d           d S )Nc                       e Zd ZddZdS )>TestSubclassingNoShapes.test_defaults_raise.<locals>._dist_genr  c                     dS r2
  r8   r3
  s      r0   r4
  zCTestSubclassingNoShapes.test_defaults_raise.<locals>._dist_gen._pdf      rr2   N)r  r5
  r8   r2   r0   rn
  r
    s(             r2   rn
  rH
  r
  r6   rC   r?  r  r  rp   rn
  s     r0   test_defaults_raisez+TestSubclassingNoShapes.test_defaults_raise  Z    	 	 	 	 	+ 	 	 	 	iAAd.@.@.@AAAAAr2   c                 x     G d dt           j                  }t          t          |fi t	          d           d S )Nc                       e Zd Zd ZdS )>TestSubclassingNoShapes.test_starargs_raise.<locals>._dist_genc                     dS r2
  r8   )rp   r\   r.   r.  s       r0   r4
  zCTestSubclassingNoShapes.test_starargs_raise.<locals>._dist_gen._pdf  r
  r2   Nr5
  r8   r2   r0   rn
  r
    #            r2   rn
  rH
  r
  r
  r
  s     r0   test_starargs_raisez+TestSubclassingNoShapes.test_starargs_raise  r
  r2   c                 x     G d dt           j                  }t          t          |fi t	          d           d S )Nc                       e Zd Zd ZdS )<TestSubclassingNoShapes.test_kwargs_raise.<locals>._dist_genc                     dS r2
  r8   )rp   r\   r.   r
  s       r0   r4
  zATestSubclassingNoShapes.test_kwargs_raise.<locals>._dist_gen._pdf  r
  r2   Nr5
  r8   r2   r0   rn
  r
    r
  r2   rn
  rH
  r
  r
  r
  s     r0   test_kwargs_raisez)TestSubclassingNoShapes.test_kwargs_raise  r
  r2   N)r   r   r   r
  r
  r   r   r  DOCSTRINGS_STRIPPEDr
  r
  r
  r
  r
  r
  r8   r2   r0   r
  r
    s        2 2 28 8 8
 [+4HII  JI [+4HII  JI< < <B B BB B BB B B B Br2   r
  r
  c                      g d} t           j        D ]k}t          t           |          }t          |t           j        t           j        f          r.| D ]+}t          t          j        ||j	                  d u            ,ld S )N)z,\s*,z\(\s*,z^\s*:)
r6   rO   r,  rE  rB   rC   r	   r
  searchr7  )badonesdistnamer?   regexs       r0   r  r    s    ---GM @ @uh''dU.0CDEE 	@  @ @	%66$>????	@ @r2   c                      t          t          j                            t          j        dd          d           t          t          j                            t          j        dd          d           d S )Nr]   r  r   r?  rZ   r   )r   r6   rn  r  rg   r  r	  r9
  r8   r2   r0   test_infinite_inputr
    sR    ((R88!<<<
377;;;;;r2   c                      t           j                            t           j                            dd          d          } t	          | d           d S r  )r6   lomaxr  rn   r   r	  s    r0   test_lomax_accuracyr
    s=    22A66AAvr2   c                      t           j                            t           j                            dd          d          } t	          | d           d S r  )r6   rf  r  rn   r   r	  s    r0   test_truncexpon_accuracyr
    sC    U-11&!<<a@@AAvr2   c                      t           j                            t           j                            dd          d          } t	          | dd           d S )NrQ  r   r  r>  rX  )r6   r)  r  r  r   r	  s    r0   test_rayleigh_accuracyr
    sF    5>,,Q22A66A3++++++r2   c                     t          j        d          5 } t          j        d           t          j                            dd           t          j                            dd           t          j                            dd           t          j                            t          j
         d           t          |           }t          |d           ddd           dS # 1 swxY w Y   dS )zregression test for gh-6219T)rv  alwaysry   r   r~   N)rx  ry  rz  r6   r  rn   rf   r  r   rg   r  r  r   )r  number_of_warnings_throwns     r0    test_genextreme_give_no_warningsr
    s    
	 	-	-	- 3h'''R###R###R###---$'FF!.2223 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3s   B?C""C&)C&c                     d} t           j                            d          }t          |d| z  dz   d           t           j                            d          }t          || dz   d           t           j                            d          }t	          |d           t           j                            d	d
          }t          || dz  t          j        d
          z   dz   d           t           j                            d
          }t          |d| z  dz   d           t           j                            d          }t          |d| z  dz   d           d S )Ngox?r  rd   r   r~  r   r   rU  rI  r]   r  r   r8  r  r  )r6   r  rE   r   r   rg   r  )euler_gammarq  s     r0   test_genextreme_entropyr
  +  sD   $K  &&AAq}q(u5555  ##AA{QU3333  %%AA  R 00AA{1}rvbzz1A5EBBBB  $$AAr+~)6666  %%AAr+~)666666r2   c                  R   d} t           j                            | d          }t          |d           t           j                            |d          }t          ||            d} t           j                            | d          }t          |d           t           j                            |d          }t          ||            d} t           j                            | d          }t          |d           t           j                            |d          }t          ||            d S )	Nr   r  g'b%4gQ@r
  gؗҜ;r   g.l6?)r6   r  r  r   r  )r\   rL   r  s      r0   test_genextreme_sf_isfr
  B  s   2 	AAv&&AA-...				a	(	(BBAAu%%AA()))				a	'	'BBAAq!!AA-...				a	#	#BBr2   c                  l    d} t           j                            | dd          }t          |d           d S )Nr  rd   r   gH&8>)r6   rW	  r  r   )probr  s     r0   test_burr12_ppf_small_argr
  n  s9    D|a++H H455555r2   c                     t          j        ddd          dd         } t          j                            | dd          }t          j        g d	          }t          ||d
           t          j                            | dd          }t          j        g d          }t          ||d
           t          j                            | dddd          }t          j        g d          }t          ||d
           t          j                            | dd          }t          j        g d          }t          ||d
           t          j                            | dd          }t          j        g d          }t          ||d
           t          j                            | dddd          }t          j        g d          }t          ||d
           dS )z
    All values are calculated using the independent implementation of the
    ROOT framework (see https://root.cern.ch/).
    Corresponding ROOT code is given in the comments.
    r	  rV  rM  Nr   rU  r}   )r  r@  )gC,d	Ɣ?gH㸘?g5?gM"M#w?gɫs^?g @?gƴ?g@w?ɫs^?|?q ?g C?r
  r
  gJó?g,BV\ۤ?g;?g#ek?g%ǓE?g(Ȍx?g>J>r_  r   rV  )g#{`?gdf?g Jq?gSS){?g'	w?uL? T)?cAJ?GTn?R1#?gA]P?r
  r
  r
  r
  gvӢ?gKq?gL?g
	N<!?gAw>ry   )r  r@  rb   rc   )g=aO}?gI8?g#T?aW)?ǓI?
J?E?d۳?GTn?8?R1#?kP?g(*T?r
  r
  r
  r
  r
  r
  r
  r
  )gD
)?g:3P?g9?g?S[?r
  gOqx?gD
)?g9?gɫs^?gK?gX?g3<֌?gM+?gyS
c?gI`s?g辜?g{i ?g^0?g?#c?)g%r?gc@v?ghtj}?g(˔^?gHK4U?r
  ğ@ _?y}D?焂Rr/?N?YjhG?a0L?4f?<@?@CH?g	ސF?g5+-#?g?g?q ?r
  )g}'v?r
  g*V?r
  gr/0+?r
  g[8	?r
  gΥ?r
  gY?r
  g#)a?r
  g?̔?r
  g]ؚ?r
  g|c ?r
  )rg   rZ  r6   crystalballrf   r   r   rn   )r  
calculatedrU   s      r0   test_crystalball_functionr
  |  s<    	D#r""3B3'A "&&qsc&::Jx & & & ' 'H
 Hju5555 "&&qsc&::Jx 3 3 3 4 4H
 Hju5555 "&&qscs#&NNJx $ $ $ % %H
 Hju5555 "&&qsc&::Jx K K K L LH Hju5555 "&&qsc&::Jx # # # $ $H
 Hju5555 "&&qscs#&NNJx K K K L LH Hju555555r2   c                     t          j        g d          } t          j        g d          }t          j        g d          }t          j                            d| |          }t          ||d           t          j        g d          }t          j        dd	t           j        d
dg          }||z  }t          j                            d| |          }t          ||d           t          j        t           j        t           j        t           j        ddg          }||z  }t          j                            d| |          }	t          ||	d           t          j        t           j        t           j        t           j        t           j        dg          }||z  }
t          j                            d| |          }t          |
|d           t          j        t           j        t           j        t           j        t           j        dg          }||z  }t          j                            d| |          }t          ||d           t          j        t           j        t           j        t           j        t           j        dg          }||z  }t          j                            d| |          }t          ||d           dS )zg
    All values are calculated using the pdf formula and the integrate function
    of Mathematica
    )r}   rU  rV  r}   rV  )rV  rV  r}   r  r  )rU  rU  rU  rU  rU  r   r_  r   )gԚh@g[&@gͪ@g2dQ@gn6-@g?ޫV&̿g BgQCRgQF\ jr   g
@gn(@rd   g?Җ)r   gMg'#@r   g('UHr   N)rg   r   r6   r
  r_	  r   r  )r  r@  expected_0th_momentcalculated_0th_momentr  r.   expected_1th_momentcalculated_1th_momentexpected_2th_momentcalculated_2th_momentexpected_3th_momentcalculated_3th_momentexpected_4th_momentcalculated_4th_momentexpected_5th_momentcalculated_5th_moments                   r0   !test_crystalball_function_momentsr    sg    8---..D
***++A (#<#<#<==!-33AtQ??')>UKKKK 8DDDEED
(HbfiCDDAd(!-33AtQ??')>UKKKK
"&"&"&&(;<<Ad(!-33AtQ??')>UKKKK
"&"&"&"&*=>>Ad(!-33AtQ??')>UKKKK
"&"&"&"&':;;Ad(!-33AtQ??')>UKKKK
"&"&"&"&(;<<Ad(!-33AtQ??')>UKKKKKKr2   c                     t          j        dd          } |                                 }d\  }}}t          j        |||          }t          t          |                     |                    |          }t          ||d           d S )Nrd   r   )ir9  r  r  r   )	r6   r
  rE   rg   rZ  r   r   rf   r   )cbrF  rc  rd  rs  r\   r  s          r0   test_crystalball_entropyr    sy    		1a	 	 B::<<D"IBA
BAAT"&&))__a((DD$T******r2   c                      dd} t          j        g d          }t          j                            |d|           \  }}}t          |dd           |dk    sJ t          |d	d           d
S )a?  
    Test fitting invweibull to data.

    Here is a the same calculation in R:

    > library(evd)
    > library(fitdistrplus)
    > x = c(1, 1.25, 2, 2.5, 2.8,  3, 3.8, 4, 5, 8, 10, 12, 64, 99)
    > result = fitdist(x, 'frechet', control=list(reltol=1e-13),
    +                  fix.arg=list(loc=0), start=list(shape=2, scale=3))
    > result
    Fitting of the distribution ' frechet ' by maximum likelihood
    Parameters:
          estimate Std. Error
    shape 1.048482  0.2261815
    scale 3.099456  0.8292887
    Fixed parameters:
        value
    loc     0

    r8   r   c                 ,    t          | |||dd          S )Nr  )r.  dispxtolftol)r$   )r   x0r.  r  s       r0   	optimizerz&test_invweibull_fit.<locals>.optimizer   s    D"4dUKKKKr2   )r   r  rd   r  r  r   r}  r   r   r?  r]   rW  @   c   )r   r  g`?r  r   g [@N)r8   r   )rg   r   r6   r"  r   r   )r  r\   r  rb   rc   s        r0   test_invweibull_fitr    s    .L L L L 	HHHIIA$((i(HHMAsEAxd++++!8888E8$//////r2   ))r   r  g7Ըh?)r   r  gz]r>)r   g     "@goBڱ9)r  r  g$=cC;c                 j    t           j                            | |          }t          ||d           d S r   )r6   r"  r  r   )r\   r  rU   r  s       r0   test_invweibull_sfr     s7     ""1a((HHhU333333r2   zp, c, expected)ry   r  g9?)geK<r   g@c                 j    t           j                            | |          }t          ||d           d S r   )r6   r"  r  r   )rw  r  rU   r  s       r0   test_invweibull_isfr  )   s7     ##Aq))HHhU333333r2   z	df1,df2,x)r   r  rU  r  r   r  r  r  r  c                 ^   d}t           j                            || |          }t           j                            || ||          }t	          ||d           t           j                            || |          }t           j                            || ||          }t	          ||d           d S )Nr   r~  r   r  )r6   rq  rn   r  r   rf   )df1df2r\   r  expected_cdfcalculated_cdfr   calculated_pdfs           r0   test_ncf_edge_caser  1   s     
B7;;q#s++LY]]1c333NL.u==== 7;;q#s++LY]]1c333NL.t<<<<<<r2   c                  l    t           j                            ddd          } t          | dd           d S )Nrd   r  r   g     `E@r~  r   )r6   r  r  r   )rA  s    r0   test_ncf_variancer  G   s6     		aAAAu5))))))r2   c                      t           j                            dddd          } d}t          |t	          j        | d                     d S )Nr  r  r
  gffffff>@g&4I,)?)decimals)r6   r  rn   r   rg   round)	scipy_val	check_vals     r0   test_ncf_cdf_spotcheckr!  R   sG    
 	b!R..IIIrx	A>>>?????r2   r\  z(On some 32-bit the warning is not raisedc                     t          j        ddd          } d| d<   dt          j        t                    5  t          j        j        | gR  }fd| D             }d d d            n# 1 swxY w Y   t          ||           d S )Nr   r   r  r  )rZ   rd   r   r   r   c                 >    g | ]}t          j        j        |gR  S r8   )r6   r  r  )r>   xipars     r0   r@   z,test_ncf_ppf_issue_17026.<locals>.<listcomp>e   s-    222"eimB%%%%222r2   )	rg   rZ  r   r  r{  r6   r  r  r   )r\   r  q0r%  s      @r0   test_ncf_ppf_issue_17026r'  \   s     	Aq#AAaD
C	n	%	% 3 3IM!"c"""22222223 3 3 3 3 3 3 3 3 3 3 3 3 3 3 Ars   &A**A.1A.c                   2    e Zd Zd Zd Zd Zd Zd Zd ZdS )TestHistogramc                 J   t           j                            d           t          j        g dd          }t	          j        |          | _        t          j                            dddd	          }t          j        |d
          }t	          j        |          | _	        d S )Nr4  )r   rd   rd   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r?  r?  rQ  r?  binsrU  r  r  {   r;  r<  )
rg   r   r   	histogramr6   rD   templater  r   norm_template)rp   r.  r   norm_histograms       r0   r6  zTestHistogram.setup_methodj   s    
	t L "@ "@ "@FGI I I	*955z~~#Su3~OOd444"/??r2   c                    t          j        g d          }t          j        g d          }t          | j                            |          |           t          | j                            d          d           t          | j                            d          d           t          | j                            d          d           t          | j                            d          d           t          j        d	d
d          }t          | j                            |          t          j
                            |dd          d           d S )Nr~   ry   rU  r  r}   r  rV  r  r  r  rV        @r<  rv  r  rP  r(        !@r  r`  )r~   r~   rN  rN  {Gz?r6  Q?r7  {Gz?r8  r  r  r8  r8  r7  r7  r7  r7  r~   r~   r(  r7  r5  r  r~   r  r   rd   r]   rU  r  ra   rZ   r   )rg   r   r   r   r/  rf   r   rZ  r0  r6   r  )rp   r  
pdf_valuesr\   s       r0   rS  zTestHistogram.test_pdfz   sX    M M M N NZ !I !I !I J J

 	))&11:>>> 	DM--c22H===DM--c22H=== 	DM--c22H===DM--d33X>>>KAr""*..q11
qc==C	I 	I 	I 	I 	I 	Ir2   c                 6   t          j        g d          }t          j        g d          }t          | j                            |          |           t          | j                            |dd                   |dd                    t          j        ddd          }t          | j                            | j                            |                    |           t          j        ddd          }t          | j                            | j                            |                    |           t          j        d	dd
          }t          | j                            |          t          j
                            |dd          d           d S )Nr3  )r~   r~   r~   ri  rN  r6  r7  
ףp=
?Q?{Gz?r  ry   r  (\?RQ?=
ףp=?)\(?r	  rU  rU  rd   r   rU  r  r^   r~   r   r]   r  ra   rZ   r   )rg   r   r   r   r/  rn   r  rZ  r0  r6   r  )rp   r  
cdf_valuesr\   s       r0   r  zTestHistogram.test_cdf_ppf   s    M M M N NZ !M !M !M N N

 	))&11:>>>))*QrT*:;;VAbD\JJJ KS#&&))$-*;*;A*>*>??CCCKS#&&))$-*;*;A*>*>??CCCKAr""*..q11
qc==C	I 	I 	I 	I 	I 	Ir2   c                 :   d}| j                             |d          }t          t          j        |dk               d           t          t          j        |dk              d|z  d	           t          t          j        |d
k              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |d k              d!|z  d	           t          t          j        |d"k              d#|z  d	           t          t          j        |d$k              d%|z  d	           t          t          j        |d&k              d|z  d	           t          t          j        |d&k              d|z  d	           t          t          j        |d&k              d           d S )'Nr  r-  r  rU  r~   r}   rN  r  r   r  r6  rV  r7  rZ   r  r;  r  r<  r  r=  rV  r  r   r4  ry   r<  r  rv  r>  r  r?  rP  r@  r(  rA  r5  r	  r  )r/  r   r   rg   rn  r   )rp   rs  r  s      r0   rK  zTestHistogram.test_rvs   s   """<<RVFSL))3///v}--x!|#FFFFv}--x!|#FFFFv}--x!|#FFFFv}--x!|#FFFFv}--x!|#FFFFv}--x!|#FFFFv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHRVFSL))3/////r2   c                     t          d          D ]R}t          | j                            |          t	          j        dd                              |          d           Sd S )Nr   rU  r  r   r   )r   r   r0  r_	  r6   r  r  r  s     r0   r	  zTestHistogram.test_munp   sx    q 	G 	GAD.44Q77!JsC0077::G G G G G	G 	Gr2   c                     t          | j                                        t          j                            dd          d           d S )NrU  r  ra   r   r   )r   r0  rE   r6   r  ru   s    r0   rr  zTestHistogram.test_entropy   sT    *2244
**s#*>>T	K 	K 	K 	K 	K 	Kr2   N)	r   r   r   r6  rS  r  rK  r	  rr  r8   r2   r0   r)  r)  i   s        @ @ @ I I I4I I I,0 0 0,G G G
K K K K Kr2   r)  c                     ddgg d}} t          j        | |fd          }t          j                            |                    ddg          ddg           |                                dk    sJ t          j        | |fd          }t          j                            |                    ddg          d	           |                                d
k    sJ d}t          t          |          5  t          j        | |f          }|                                d
k    sJ 	 d d d            n# 1 swxY w Y   t          j        | g df          }|                                dk    sJ d S )Nr   )r   r   r  F)r  ry   r  rr	  Tg'^P?g     H@z(Bin widths are not constant. Assuming...r  r  )	r6   rD   rg   r	  r   rf   r  r
   r{  )countsr,  r?   r  s       r0   test_histogram_non_uniformrH     s   FLLLDFvtne<<<DJtxxc
33c6]CCC;;==Avtnd;;;DJtxxc
33V<<<;;==F"""" 9G	nG	4	4	4 ' '!64.11{{}}&&&&&' ' ' ' ' ' ' ' ' ' ' ' ' ' '
 vyyy122D;;==As   11D//D36D3c                   f    e Zd Zd Zej                            dddg          d             Zd ZdS )TestLogUniformc                 ~   t           j                            d          }t          j        dd          }|                    d|          }t           j                            d          }t          j        dd          }|                    d|          }t          ||           t          j        t          j	        |          d          \  }}d|
                                cxk    r|                                cxk    rd	k    sn J t          j        t          j        |          d
z
            dk    sJ d S )N   0o[ r_  r   r  r  r]   r+  rK  iL  r   )rg   r   r   r6   
loguniformr   
reciprocalr   r.  log10r  rj  r   r  )rp   r   rQ  r   rv2r   rI  r   s           r0   
test_aliaszTestLogUniform.test_alias   s    i##K00h00ff%cf22i##K00x11wwEw44c""",rx}}2666adhhjj6666DHHJJ6666$666666vbioo,--333333r2   r  mler  c                 D   t           j                            d          }t          j                            ddd|          }t          j                            ||          \  }}}}|dk    sJ t          j                            |d|          \  }}}}|dk    sJ d S )	NrL  rZ   r   r   r  r  rd   r   )rg   r   r   r6   rM  r   r   )rp   r  r   r   r.   r/   rb   rc   s           r0   test_fit_overridez TestLogUniform.test_fit_override   s     i##K00""33"GG +//F/CC1c5zzzz +//Af/MM1c5zzzzzzr2   c                    t           j                            d          }d\  }}t          j        ||          }|                    ddd          }t          |                    |                    |                    |           |	                    d          }t          |                    |                    |                    |           dt          j
        dd	          z  }|                    |          }t          |d d
         |dd          z  d           ||z
  t          j        |          t          j        |          z
  z  }	t          |                                |	           d S )Nl   eVi
P )gN~hgZbtir   r   r   r:  r  i8r  r   r]   )rg   r   r   r6   rM  rT  r   rn   r  r   r  rf   r  r|  )
rp   r   r.   r/   r?   rn   r   r\   rf   r|  s
             r0   test_overflowzTestLogUniform.test_overflow !  s<    i##$78811%% kk!QTk**#//555hhDh!!#//555 4%%%hhqkkCRCQRR("--- Aq		BF1II-.		T*****r2   N)	r   r   r   rQ  r   r   r   rT  rV  r8   r2   r0   rJ  rJ     sd        4 4 4" [Xt}55
 
 65
+ + + + +r2   rJ  c                      e Zd Zd Zej                            dddgddgddgg          d	             Zej                            d
ddg          d             Zej                            dg d          d             Z	ej                            dg d          d             Z
ej                            dg d          d             Zej                            dg d          d             Zej                            dg d          d             Zej                            dg d          d             Zej                            dg d          d             Zd S )!	TestArgusc                     t           j                            ddd          }t          t          j        d                                          |                                d           d S )Nr<  ra  E  r  r   rX  )r6   argusr   r   r|  r  s     r0   test_argus_rvs_large_chiz"TestArgus.test_argus_rvs_large_chi!  sR    KOOBSsO;;EKOO0022AFFHHaHHHHHHr2   zchi, random_staterZ   rZ  r     r     c                     t           j                            |d|          }t          j        |d|f          \  }}t	          |dk               d S )Nra  r  r[  r   r6   r[  r   r  r	   )rp   r  r   r\   r   rw  s         r0   rK  zTestArgus.test_rvs!  sN     KOOCcOEE|Aw001Dr2   r  rA  r  c                     t           j                            |dd          }t          j        |d           \  }}t	          |dk               d S )Nra  ie r  c                     dd| dz  z
  dz  z
  S )Nr   rd   r  r8   r   s    r0   rM   z.TestArgus.test_rvs_small_chi.<locals>.<lambda>-!  s    a!Q$h#->)> r2   r   r`  )rp   r  r  r   rw  s        r0   test_rvs_small_chizTestArgus.test_rvs_small_chi'!  sN    
 KOOCcO??|A>>??1Dr2   zchi, expected_mean))r   g щi?)r]   g.憃?)r  g\paP?)r  g	?)r  g,6?c                 l    t           j                            |d          }t          ||d           d S )Nr   r  r   r   )r6   r[  r|  r   )rp   r  expected_meanr@  s       r0   r  zTestArgus.test_mean1!  s9     KS**=u555555r2   zchi, expected_var, rtol))r   gLH'B?r   )r]   go$?r1  )r  g
=>r  )r  g2W>r  )r  gb~P>r  c                 l    t           j                            |d          }t          |||           d S )Nr   r  r   )r6   r[  r  r   )rp   r  expected_varr   rA  s        r0   rz  zTestArgus.test_var<!  s6     KOOCqO))<d333333r2   zchi, expected, rtol))r  gwM?r~  )ry   gj?r~  )rZ   gHEA`!?r~  )r{   gcف>r   )r_  gF=r~  )r  g߹Q#B=r~  )r  g0ޟ<r~  )rA  g*W%:r   c                 D    t          t          |          ||           d S rL  )r   r"   )rp   r  rU   r   s       r0   test_argus_phi_small_chiz"TestArgus.test_argus_phi_small_chiG!  s%     	
3======r2   zchi, expected))ry   )g-\/?g+p7c?g5Ϧ\?)r  )g
f?gi{?ٸ?gZ@7?)rZ   )gB	?g]?gR{?)r{   )glͅw?g,?g[Z=?)r_  )gz,?g]?gѪ1?)r  )g8<?gE-?gI?)r  )g~7?g7B.?g9?)rA  )g;?g9B.?g}5?c                     t          j        g d          }t          t          j                            ||          |d           d S )NrZ   ry   r  r   r   )rg   r   r   r6   r[  rf   rp   r  rU   r\   s       r0   test_pdf_small_chizTestArgus.test_pdf_small_chiT!  B     H___%%3//FFFFFFr2   ))ry   )gQ߹?e?grJ,?g򺗄?)r  )gΎd?g?gh?)rZ   )g|
o?gvb?g+@?)r{   )g̈́On?ge?gC|[3?)r_  )g!?m?g{jiH?gu53?)r  )g~m?g0-.?g3?)r  )g~m?g7;B.?gŗ3?)rA  )g~m?g9B.?gŗ3?c                     t          j        g d          }t          t          j                            ||          |d           d S )Nrk  r~  r   )rg   r   r   r6   r[  r  rl  s       r0   test_sf_small_chizTestArgus.test_sf_small_chic!  sB     H___%%q#..uEEEEEEr2   ))ry   )g+&?gk?gμm/?)r  )g?CL\f?g^N?g]AͭR?)rZ   )ga>$?g;Lf?gaW?)r{   )gx?g 43n?gwY?)r_  )go7🤎?g
+-oGn?gIQ9Y?)r  )gT?gGn?g@̋Y?)r  )gU?g{Gn?giG͋Y?)rA  )gDU?g {Gn?gH͋Y?c                     t          j        g d          }t          t          j                            ||          |d           d S )Nrk  r  r   )rg   r   r   r6   r[  rn   rl  s       r0   test_cdf_small_chizTestArgus.test_cdf_small_chir!  rn  r2   ))ry   )gQ)?g6{?r  )gB`"۹?)g?g8%?r1  )rZ   )g388?gV%?r   )r{   )g*j?gRS%?r   )r_  )g!|?gZ%?r   )r  )gy[|?gG%?r   )r  )g"3|?gW%?r   )rA  )g!3|?gW%?r   c                 l    t           j                             |d          }t          |||           d S )NrD  rX  r   )r6   r[  r   )rp   r  rU   r   rJ  s        r0   test_stats_small_chizTestArgus.test_stats_small_chi!  s9     kT22XD111111r2   N)r   r   r   r\  r   r   r   rK  rc  r  rz  ri  rm  rp  rr  rt  r8   r2   r0   rX  rX  !  s       I I I
 [0#J#J#J3
  
  

 [UT4L11  21 [18 8 89 96 69 96
 [6B B BC C4 4C C4
 [2D D DE E> >E E> [	M 	M 	M	N 	NG G	N 	NG
 [	N 	N 	N	O 	OF F	O 	OF
 [	P 	P 	P	Q 	QG G	Q 	QG
 [	C 	C 	C	D 	D2 2	D 	D2 2 2r2   rX  c                   d   e Zd Zd Zd Zej                            dg d          d             Zej                            dg d          d             Z	d Z
ej                            d	
          ej                            dg d          ej                            dg d          ej                            dg d          d                                                 Zej                            dg d          ej                            dg d          d                         ZdS )TestNakagamic                 n    d}d}t           j                            ||          }t          |d           d S )Nr  r  gM+)r6   nakagamir   r   )rp   r
  r\   r[  s       r0   r\  zTestNakagami.test_logpdf!  s<     ~$$Q++122222r2   c                     d}d}t           j                            ||          }t          |dd           t           j                            ||          }t          ||d           d S )Nr  rV  g"S+:r   r   )r6   rx  r  r   r  )rp   r
  r
  r  r  s        r0   r  zTestNakagami.test_sf_isf!  sm     ^r2&&1>>>>^B''BU++++++r2   zm, ref))r   g|Bd븿)ry   r  )r]   g/ۿc                 d    t          t          j                            |          |d           d S )Ng^~z=r   r   r6   rx  rE   rp   r@  r  s      r0   rr  zTestNakagami.test_entropy!  s/      	..q113WEEEEEEr2   ))r  g}Ô%I)r  gq_)g    ScAgB4U)g    cAgu1U)r  gb>%)r  gWҙ\c                 `    t          t          j                            |          |           d S rs   r{  r|  s      r0   test_extreme_nuzTestNakagami.test_extreme_nu!  s*    
 	..q11377777r2   c                     t          j        t          j                            d                    sJ t          j        t          j                            d                    sJ d S )Nr  r  )rg   r  r6   rx  _entropyru   s    r0   test_entropy_overflowz"TestNakagami.test_entropy_overflow!  sT    {5>22599:::::{5>226::;;;;;;;r2   z+Fit of nakagami not reliable, see gh-10908.r  r
  )r  r  r~  rb   )r|   r]   #   rc   )r  r   r  c                   
 d
t           j                            
|||d          t           j                                      \  }}}t	          ||d           t	          ||d           t	          ||d           fd}
fd}
fd}	t	           ||||          d	d
           t	           ||||          d	d
           t	           |	|||          d	d
           d S )Nr^   9  r   r
  rb   rc   r   r  r   c                     d| z  dz   t          j        d|z
  z            z  d| z  |dz  z  t          j        |z
            z  z   S )Nr   r   rd   rg   rn  )r
  rb   rc   r  s      r0   	dlogl_dnuz(TestNakagami.test_fit.<locals>.dlogl_dnu!  sR    UQY"&GcM):";";;d5!8mbfWs]&;&;;< =r2   c                     dt          j        |           z   t          d|           z
  z  dt          j        t          j        |z
  |z                      z  z   t          j        |z
  |z  dz            z
  S )Nr   r   rd   )rg   r  r   rn  r
  rb   rc   rs  r  s      r0   
dlogl_dlocz)TestNakagami.test_fit.<locals>.dlogl_dloc!  sv    RVBZZ)Ar*:*::;rvw}&=>>???@fw}59::; <r2   c                 h    dz  | z  |z  d| z  |dz  z  t          j        |z
  dz            z  z   S )Nr   rd   r   r  r  s      r0   dlogl_dscalez+TestNakagami.test_fit.<locals>.dlogl_dscale!  sG    !GbL5("fuz)BFGcMa3G,H,HHI Jr2   r   r_  r   )r6   rx  r   r   r   )rp   r
  rb   rc   nu_estloc_est	scale_estr  r  r  rs  r  s             @@r0   r  zTestNakagami.test_fit!  s[    .$$!+0t % E E%*^%7%7%@%@"----3////	5s3333	= 	= 	= 	= 	=	< 	< 	< 	< 	< 	<
	J 	J 	J 	J 	J 	J 			&'9==qtLLLL

67I>>MMMMVWi@@!$OOOOOOr2   c                    d}d}t           j                            ||||d          }t           j                            ||          \  }}}t	          j        |          }	t	          j        t	          j        ||z
  dz                      }
t          ||d           t          ||	d           t          ||
d           d S )	Nry   r^   r  r  r  rd   r  r   )	r6   rx  r   r   rg   r  r)  r|  r   )rp   rb   rc   r
  rv  r  r  r  r  loc_theo
scale_theos              r0   test_fit_nuzTestNakagami.test_fit_nu!  s    
 .$$!+0t % E E%*^%7%7B%7%G%G" 6'??WRWg&7A%=>>??
....5555	:D999999r2   N)r   r   r   r\  r  r   r   r   rr  r~  r  r  r  r  r8   r2   r0   rv  rv  !  s       3 3 3", , ,& [X	$ 	$ 	$% %F F	% %F [X	D 	D 	DE E8 8	E E8< < < [KLL[T???33[UNNN33[Wkkk22P P 32 43 43 MLP8 [UNNN33[Wkkk22: : 32 43: : :r2   rv  c                        e Zd Zd Zd Zd ZdS )TestWrapCauchyc                 L   t          j        ddgddgg          }t          j        dgdgg          }t          j                            ||          }|j        dk    sJ d t          j        ||f          D             }t          |                                |d	
           d S )NQ?r   ry   rc  rU  r  r  c                 T    g | ]%\  }}t           j                            ||          &S r8   )r6   
wrapcauchyrn   )r>   r  r9	  s      r0   r@   z>TestWrapCauchy.test_cdf_shape_broadcasting.<locals>.<listcomp>"  s?     < < <%b" )--b"55 < < <r2   r   r   )	rg   r   r6   r  rn   rC  nditerr   r5	  )rp   r  r\   rw  scalar_valuess        r0   test_cdf_shape_broadcastingz*TestWrapCauchy.test_cdf_shape_broadcasting	"  s     HtTlS$K011HsecU^$$  A&&w&    < <)+Aq6):):< < <		=u======r2   c                 ~    t           j                            t          j        d          }t          |dd           d S )Nr  ry   r~  r   )r6   r  rn   rg   rh   r   r  s     r0   test_cdf_centerzTestWrapCauchy.test_cdf_center"  s7      --3U++++++r2   c                    d}d}d}t           j                            ||g|          }d|z   d|z
  z  }t          |d         t	          j        |t	          j        |dz            z            t          j        z             t          |d         dt	          j        |t	          j        t          j        |dz  z
            z            t          j        z  z
             d S )NrU  r  rc  r   r   rd   )r6   r  rn   r   rg   arctantanrh   )rp   r  r  r  rw  crs         r0   r]  zTestWrapCauchy.test_cdf"  s      "b1--!ea!e_!bi26"Q$<<88>???!a")Brvbebdl/C/C,C"D"DRU"JJKKKKKr2   N)r   r   r   r  r  r]  r8   r2   r0   r  r  "  sF        
> 
> 
>, , ,L L L L Lr2   r  c                       G d dt           j                  }  | d          }t          t          d          5  |                                 d d d            d S # 1 swxY w Y   d S )Nc                       e Zd Zd ZdS )/test_rvs_no_size_error.<locals>.rvs_no_size_genc                     dS r   r8   ru   s    r0   _rvsz4test_rvs_no_size_error.<locals>.rvs_no_size_gen._rvs&"  s    1r2   N)r   r   r   r  r8   r2   r0   rvs_no_size_genr  %"  s#        	 	 	 	 	r2   r  rvs_no_sizer
  z_rvs\(\) got (an|\d) unexpectedr  )r6   rC   r?  r  r   )r  r  s     r0   test_rvs_no_size_errorr  #"  s        %-    "/}555K	y(J	K	K	K                   s   AA!$A!zdistname, argsc                 n   | t           v rt          j        d|  d           t          t          |           }t          |t          j                  rt          |          dk    rA |j        | \  }}t          |t          j                   t          |t          j                   d\  }} |j        g |||R  \  }}t          |t          j                   t          |t          j                   d S  |j        | \  }	}
t          |	t          j                   t          |
t          j                   d S )Nz6skipping test for the support method for distribution .r   r[  )$skip_test_support_gh13294_regressionr   r   r,  r6   rE  rC   r  supportr   rg   r  )r
  r.  r?   a0b0r5  r6  a1b1r.   r/   s              r0   test_support_gh13294_regressionr  /"  s8   777 0$,0 0 0 	1 	1 	15(##D$+,,  t99>>!T\4(FBRV$$$RV$$$
 f2t2T26222BR   R     t|T"1QQr2   c                  \   t           j                            g dg d          \  } }t          j        t          j         t          j         t          j         t          j        g          }t          j        t          j        t          j        t          j        t          j        g          }t          | |           t          ||           | j        |j        k    sJ |j        |j        k    sJ t           j                            g g           \  }}t          j        g           t          j        g           }}t          ||           t          ||           |j        |j        k    sJ |j        |j        k    sJ t           j                            g ddg          \  }}	t          j        dt          j        gz            }
t          j        dt          j        gz            }t          ||
           t          |	|           |j        |
j        k    sJ |	j        |j        k    sJ d S )N)r   r   r   r   )r   r   r   r   r   r   )	r6   r  r  rg   r   r  r  r   rC  )r  r  ex_a0ex_b0r  r  ex_a1ex_b1r  r  ex_a2ex_b2s               r0   ,test_support_broadcasting_gh13294_regressionr  J"  s   Zmmm<<FBHrvgw899EHbfbfbfbf566EUU8u{""""8u{""""ZB''FB8B<<"5EUU8u{""""8u{""""Zrd33FBHQxZ  EHQxZ  EUU8u{""""8u{""""""r2   c                  2   ddg} dgdgdgg}t          t          j                            | |          ddgddgddgg           t	          j        d          } t	          j        d          }t          j                            | |          j        dk    sJ d S )	Nr~   rU  r}   rV  r  r  r<   r"  )r   r6   r  r  rg   r4	  rC  ra   s     r0   *test_stats_broadcasting_gh14953_regressionr  c"  s    r(CTB4"EU++r2hR2r(-KLLL
(5//CHVE:>>#u%%+v555555r2   )gn!	g:I"<)gQ	@gE?c                     t          t          j                            |           |           t          t          j                            |            |           d S rs   )r   r6   cosinern   r  )r\   rU   s     r0   test_cosine_cdf_sfr  q"  sJ     EL$$Q''222ELOOQB''22222r2   ))r  gkM6O)r;  g0ӭ!	)r
  g;'u(@c                     t          t          j                            |           |           t          t          j                            |           |            d S rs   )r   r6   r  r  r  )rw  rU   s     r0   test_cosine_ppf_isfr  y"  sL    
 EL$$Q''222EL$$Q''(33333r2   c                      t           j                            t          j         t          j        g          } t          | d           d S )NgrB)r6   r  r   rg   rh   r   )r[  s    r0   test_cosine_logpdf_endpointsr  "  s:    <//D d./////r2   c                      d t           D             } d t          D             }| |k    sJ d t          D             }d t          D             }||k    sJ d S )Nc                 B    h | ]\  }}t          |t                    |S r8   )rE  rI   r>   r  r   s      r0   	<setcomp>z*test_distr_params_lists.<locals>.<setcomp>"  s:     4 4 474'c224$ 4 4 4r2   c                     h | ]\  }}|S r8   r8   r  s      r0   r  z*test_distr_params_lists.<locals>.<setcomp>"  s    AAAgdATAAAr2   c                     h | ]\  }}|S r8   r8   r  s      r0   r  z*test_distr_params_lists.<locals>.<setcomp>"  s    333wtQd333r2   c                     h | ]\  }}|S r8   r8   r  s      r0   r  z*test_distr_params_lists.<locals>.<setcomp>"  s    999'$999r2   )r   r    r   r   )discrete_distnamesinvdiscrete_distnamescont_distnamesinvcont_distnamess       r0   test_distr_params_listsr  "  s    4 4l 4 4 4AAAAA!6666633(333N99[999.......r2   c                      t           j                            dd           t           j                            dd          dk    sJ t           j                            dd          dk    sJ d S )Nr   rY   r  r   )r  r.   rV  )r6   r  _statsr  r_	  r8   r2   r0   test_moment_order_4r  "  sr     
NAs+++ >  qA ..#5555 >1%%,,,,,,r2   c            
          e Zd Zej        d             Zej                            dg d          d             Zej                            dg d          d             Z	ej                            d ej
        d	d
ej        j                   ej
        ddej        j                   ej
        ddej        j                  g          d             ZdS )TestRelativisticBWc                     t          j        t          t                    j        dz            }t           j        j                            |j        d          }|S )a&  Sample data points for pdf computed with CERN's ROOT

        See - https://root.cern/

        Uses ROOT.TMath.BreitWignerRelativistic, available in ROOT
        versions 6.27+

        pdf calculated for Z0 Boson, W Boson, and Higgs Boson for
        x in `np.linspace(0, 200, 401)`.
        z-data/rel_breitwigner_pdf_sample_data_ROOT.npyzx,pdf,rho,gammar  r  r  s     r0   ROOT_pdf_sample_dataz'TestRelativisticBW.ROOT_pdf_sample_data"  sO     wNN!;<
 
 w))$&8I)JJr2   zrho,gamma,rtol))qVEB@gj+@r  )FC@Gz @r~  )ND@_LU?rT  c                     ||d         |k    |d         |k    z           }|d         |d         }}t          |t          j                            |||          |           d S )NrhorZ  r\   rf   r  r   )r   r6   rel_breitwignerrf   )rp   r  r  rZ  r   r   r\   rf   s           r0   test_pdf_against_ROOTz(TestRelativisticBW.test_pdf_against_ROOT"  s     $!%(C/#G,57
 cDK3&**1c*??d	
 	
 	
 	
 	
 	
r2   zrho, Gamma, rtol))r  r  rT  )r  r  rT  )r  r  g&.>c                    d }t          j        ddd          }t          j                            |||          }t          j                            |||          } ||||z  |          }t          |||           d S )Nc                    t          j        |dz  |dz  |dz  z   z            }dt          j        d          z  |z  |z  |z  t           j        t          j        |dz  |z             z  z  }|| dz  |dz  z
  dz  |dz  |dz  z  z   z  S r  )rg   r)  rh   )Err  GammarZ  rY   s        r0   rf   zFTestRelativisticBW.test_pdf_against_simple_implementation.<locals>.pdf"  s    GAqDAqD5!8O455ERWQZZ!#e+e3EBGAqD5L1113AA1q(1a4q=899r2   r   r  r]   r  r   )rg   rZ  r6   r  r  rf   r   )	rp   r  r  r   rf   rw  r\   r   r  s	            r0   &test_pdf_against_simple_implementationz9TestRelativisticBW.test_pdf_against_simple_implementation"  s    	: 	: 	: KdB''!%%aE%::#''3e'<<c!SY&&St,,,,,,r2   z	rho,gammar  r  r  r  r  r  r  c                    d}t           j                            |          }t          j                            ||d|          }t          j                            |d          }t          |d         |d         f||fd           |d	         dk    sJ t          j                            |d|
          }t          |d         |d           |d	         |d         fd|fk    sJ dS )zpTests fit for cases where floc is set.

        `rel_breitwigner` has special handling for these cases.
        l   s;
rl# r   )rc   r   r   r   r   rd   r  r   r   r>  r{   N)rg   r   r   r6   r  r   r   r   )rp   r  rZ  r   r   r   r   s          r0   test_fit_flocz TestRelativisticBW.test_fit_floc"  s    $ #i##D))$((u4c ) 
 
 #''1'55QQ(3,TBBBB1v{{{{#''1U'CCA$////AAAu:------r2   N)r   r   r   r   r  r  r   r   r  r  r  r  r   r  r8   r2   r0   r  r  "  sU       ^  ^$ [ 
 
 
 
 
 
 [/ 2 2 2  - - - [FL"F&+2B   FL!50A   FL &0A  

 . . . . .r2   r  c                   Z    e Zd Zej                            dddg          d             ZdS )TestJohnsonSUr9  )r	  rW  ri  r  g={?g?5mV>gn?g\}\1@)g`fo@g$ں_@r   r   gvUgN<fj?gwCg~l
@c                 v    t          j        j         |d d         ddi}t          ||dd          d           d S )Nr   rY  rW  r~  r   )r6   r  r   )rp   r9  r   s      r0   test_moment_gh18071z!TestJohnsonSU.test_moment_gh18071#  sF     o#T"1"X>v>>T!""XE222222r2   N)r   r   r   r   r   r   r  r8   r2   r0   r  r  #  sZ        [VOJ&K L L
3 3L L
3 3 3r2   r  c                   2   e Zd Zd Zej                            dddg          ej                            dddg          ej                            dddg          ej                            dddg          d                                                 Zd	S )
TestTruncParetoc                 H   d\  }}t          j        dd          }t          j        ||                              |          }t          j        |                              |          t          j        |                              |          z  }t          ||           d S )N)?333333@r  r  )rg   rZ  r6   truncparetorf   r  rn   r   )rp   r/   r  r\   r   r  s         r0   rS  zTestTruncPareto.test_pdf#  s    1KS!!1%%))!,,l1oo!!!$$u|A':':1'='==S!!!!!r2   r   TFr  r$  fix_cc                    t           j                            d          }d\  }}}}	t          j        ||||	          }
|
                    d|          }i }|r||d<   |r|	|d<   |r||d<   |r||d	<   |rU|rS|rQ|rOd
}t          j        t          |          5  t          j        j	        |fi | d d d            d S # 1 swxY w Y   d S t          t          j        |fi | d S )Nl   Z#Lm )r  r  r   r  ra   ra  r  r   r   r   r  r
  r  )rg   r   r   r6   r  r   r   r   r  r   r   )rp   r   r  r$  r  r   r/   r  rb   rc   r?   r   r   r  s                 r0   r  zTestTruncPareto.test_fit#  s}    i##$788+1c5 A3e<<<xxSsx33 	DL 	#"DN 	DJ 	DJ 	Ky 	KU 	Ku 	KKG|7;;; 4 4!%d33d3334 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 *%*;TJJTJJJJJs   B>>CCN)r   r   r   rS  r   r   r   r  r8   r2   r0   r  r  #  s        " " " [Yu66[[4-88[WtUm44[WtUm44K K 54 54 98 76K K Kr2   r  rs   )r7  rx  r
  r^  r   pathlibr   r	  r	  ro  numpy.testingr   r   r   r   r   r	   r
   r   r   r   r   r   r?  rA  rg   r   r   numpy.lib.recfunctionsr   r5   r   scipy._lib._utilr   r[  r   r   r   r   scipy.statsr6   !scipy.stats._distn_infrastructurer   scipy.stats.distributionsscipy.specialr   r   r   scipy.stats._distr_paramsr   r   test_discrete_basicr   r    scipy.stats._continuous_distnsr!   r"   scipy.optimizer#   r$   	itertoolsr%   flagsoptimizer
  rr  r  r  r1   r9   rV   rX   r   r  r   r   r/  r1  r_  r  r  r  r  r  r  r  r:  rb  r  r  r  r  r  r  r  r  r  r  rW  rm  r  r  r  r  r  r  r  rF  r|  r  r  r  r  r  r  r  r1  rB  rL  rU  re  r  r  r  r)  rh   r  r  r  r%  r2  r9  rW  rd  rh  rl  rw  r  r  r  r  r  r  r  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r	  r#	  r?	  rD	  rI	  rP	  rf	  ri	  r	  r	  r	  r  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r	  r
  r
  r
  r
  r
  r
  r
  r
  r
  r!
  r#
  r%
  r.
  rC   r0
  r7
  r<
  rB
  rF
  r
  r  r
  r
  r
  r
  r
  r
  r
  r
  r
  r  r  r  r  r  r  r  r!  r_  r'  r)  rH  rJ  rX  rv  r  r  r  r  r  r  r  r  r  r  r  r  r  r8   r2   r0   <module>r     s)      				 



        				  J J J J J J J J J J J J J J J J J J J J J J J J  * * * * * *      " " " " " " " " 4 4 4 4 4 4       / / / / / /3 3 3 3 3 3 3 3 3 3 3 3       8 8 8 8 8 8         0 0 0 0 0 0 0 0 0 0 ; ; ; ; ; ; ; ; > > > > > > > > C C C C C C C C % % % % % % % %       i(1,  |x'M.>h.>.@.@H.L )6z'B $$ $ $ $8 8 8
  D( D( D( D( D( D( D( D(N4 4 4 44. . .. > > >? ?

6 
6? ?

69 9 9 9 9 9 9 9>G, G, G, G, G, G, G, G,T* * * * * * * *       >       &B &B &B &B &B &B &B &BR# # # # # # # #<E; E; E; E; E; E; E; E;PG G G G G G G GTCD CD CD CD CD CD CD CDLA: A: A: A: A: A: A: A:H2 2 2 2 2 2 2 2"'K 'K 'K 'K 'K 'K 'K 'KT> > > > > > > >*'D 'D 'D 'D 'D 'D 'D 'DT
C 
C 
C 
C 
C 
C 
C 
C@ @ @ @ @ @ @ @DD D D D D D D D8* * * * * * * *. G  G  G  G  G  G  G  GFK" K" K" K" K" K" K" K"\=I =I =I =I =I =I =I =I@J: J: J: J: J: J: J: J:ZG& G& G& G& G& G& G& G&TD D D D D D D D,D D D D D D D D,U< U< U< U< U< U< U< U<p%( %( %( %( %( %( %( %(P"B "B "B "B "B "B "B "BJT# T# T# T# T# T# T# T#nt: t: t: t: t: t: t: t:nJ7 J7 J7 J7 J7 J7 J7 J7Z< < < < < < < <~'* '* '* '* '* '* '* '*TO@ O@ O@ O@ O@ O@ O@ O@d/ / / / / / / /2!, !, !, !, !, !, !, !,HLE LE LE LE LE LE LE LE^i5 i5 i5 i5 i5 i5 i5 i5XP6 P6 P6 P6 P6 P6 P6 P6f9J 9J 9J 9J 9J 9J 9J 9Jx0D 0D 0D 0D 0D 0D 0D 0Df4D 4D 4D 4D 4D 4D 4D 4Dn( ( ( ( ( ( ( (VdA dA dA dA dA dA dA dAN]J ]J ]J ]J ]J ]J ]J ]J@*9 *9 *9 *9 *9 *9 *9 *9j 7271ag;		
	gbga25k""	"	
	1RU7$$	$		AbeG%%	%		GBGAqwK((	(	* + 	7271c"%i=!!7271c"%i=)))7271c"%i=)))50gbgaRUm,,,g53ru9...	9; < "WRWQruW


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#

WRWQruW%%%
&

#gbgag&&&
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eGBGAbeG,,,
-

wrwqw///
0

 '!  He8 e8 e8 e8 e8 e8 e8 e8P6 6 6 6 6 6 6 6&5 5 5 5 5 5 5 5:
8 
8 
8 
8 
8 
8 
8 
8s5 s5 s5 s5 s5 s5 s5 s5l/, /, /, /, /, /, /, /,b	E 	E 	E 	E 	E 	E 	E 	E       /G /G /G /G /G /G /G /Gd)C )C )C )C )C )C )C )CXI9 I9 I9 I9 I9 I9 I9 I9XN" N" N" N" N" N" N" N"bF@ F@ F@ F@ F@ F@ F@ F@RO6 O6 O6 O6 O6 O6 O6 O6d'C 'C 'C 'C 'C 'C 'C 'CT& & & & & & & &>$ $ $ $ $ $ $ $*E
 E
 E
 E
 E
 E
 E
 E
P) ) ) ) ) ) ) )       , , , lG lG lG lG lG lG lG lG^e, e, e, e, e, e, e, e,Pw; w; w; w; w; w; w; w;t>> >> >> >> >> >> >> >>B", ", ", ", ", ", ", ",JB& B& B& B& B& B& B& B&J6 6 6 6 6 6 6 68;" ;" ;" ;" ;" ;" ;" ;"|e. e. e. e. e. e. e. e.P. . . . . . . ..SF SF SF SF SF SF SF SFl. . . . . . . .2J/ J/ J/ J/ J/ J/ J/ J/Z3 3 3 3 3 3 3 3 [L [L [L [L [L [L [L [L|6 6 6 6 6 6 6 6(? ? ? ? ? ? ? ?,N N N N N N N NH! H! H! H! H! H! H! H!V5 5 5 5 5 5 5 54A A A A A A A AH	< 	< 	<9 9 9
! ! !* '0EFF/ / GF/
< < <*5 5 585 5 5. . .2 2 2(: : :#4 #4 #4L  	, 	, 	,   )J J JK K
A 
AK K
A  # # #  07 7 72' ' '0	- 	- 	-. *F F FG G1 1G G1
	- 	- 	-& & &9 9 9%& %& %&P- - -M M M" +
HBHo7889
HBHo7889xrx|4556
HBHk;/001	.  2 2 22 2 26 6 61 1 167 7 7: ); ; ;< <) )< <) : : :; ;
) ); ;
) ; ; ;< <! !< <!
  ( ); ; ;< <
) )< <
)
% % %*    $   
    %%   
    %%       %%   u9 u9 u9 u9 u9 u9 u9 u9p8B 8B 8B 8B 8B 8B 8B 8Bv '0DEE@ @ FE@< < <
    , , ,3 3 37 7 7.) ) )X6 6 6D6 D6 D6N+L +L +L\+ + +0 0 0D )F F FG G
4 4G G
4 )<<>? ?4 4? ?4
 !!!""""#___ = = = * * *@ @ @ CK5(E  G G G G^K ^K ^K ^K ^K ^K ^K ^KB  .3+ 3+ 3+ 3+ 3+ 3+ 3+ 3+lv2 v2 v2 v2 v2 v2 v2 v2rt: t: t: t: t: t: t: t:nL L L L L L L L8	 	 	 )?[+HII    JI 4# # #26 6 6 ;467 73 37 73
 7 7 78 84 4	8 84
0 0 0/ / /- - -(V. V. V. V. V. V. V. V.r3 3 3 3 3 3 3 3 #K #K #K #K #K #K #K #K #K #Kr2   