o 0Gf@sdZddlZeejZGdddZeZde_GdddZ e Z de _e d d Z d e _e d d Z d e _GdddZ e Zde_GdddZeZde_dS)zP Variance functions for use with the link functions in statsmodels.family.links Nc@s eZdZdZddZddZdS)VarianceFunctiona Relates the variance of a random variable to its mean. Defaults to 1. Methods ------- call Returns an array of ones that is the same shape as `mu` Notes ----- After a variance function is initialized, its call method can be used. Alias for VarianceFunction: constant = VarianceFunction() See Also -------- statsmodels.genmod.families.family cCst|}t|jtjS)z Default variance function Parameters ---------- mu : array_like mean parameters Returns ------- v : ndarray ones(mu.shape) )npZasarrayZonesshapeZfloat64selfmurDlib/python3.10/site-packages/statsmodels/genmod/families/varfuncs.py__call__s zVarianceFunction.__call__cCs t|S)< Derivative of the variance function v'(mu) )rZ zeros_likerrrr deriv.s zVarianceFunction.derivN)__name__ __module__ __qualname____doc__r r rrrr rs rz~ The call method of constant returns a constant variance, i.e., a vector of ones. constant is an alias of VarianceFunction() c@s*eZdZdZd ddZddZddZd S) Powerav Power variance function Parameters ---------- power : float exponent used in power variance function Methods ------- call Returns the power variance Notes ----- Formulas V(mu) = numpy.fabs(mu)**power Aliases for Power: mu = Power() mu_squared = Power(power=2) mu_cubed = Power(power=3) ?cC ||_dSNpower)rrrrr __init__W zPower.__init__cCstt||jS)z Power variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray numpy.fabs(mu)**self.power )rrfabsrrrr r ZszPower.__call__cCs<|jt||jd}t|dk}||d9<|S)z_ Derivative of the variance function v'(mu) May be undefined at zero. r)rrrZ flatnonzero)rrZderiirrr r jsz Power.derivNr)r rrrrr r rrrr r>s   rz> Returns np.fabs(mu) Notes ----- This is an alias of Power() rza Returns np.fabs(mu)**2 Notes ----- This is an alias of statsmodels.family.links.Power(power=2) za Returns np.fabs(mu)**3 Notes ----- This is an alias of statsmodels.family.links.Power(power=3) c@2eZdZdZd ddZddZddZd d Zd S) Binomiala Binomial variance function Parameters ---------- n : int, optional The number of trials for a binomial variable. The default is 1 for p in (0,1) Methods ------- call Returns the binomial variance Notes ----- Formulas : V(mu) = p * (1 - p) * n where p = mu / n Alias for Binomial: binary = Binomial() A private method _clean trims the data by machine epsilon so that p is in (0,1) rcCrr)n)rr"rrr rrzBinomial.__init__cCst|tdtS)Nr)rclip FLOAT_EPSrprrr _cleanszBinomial._cleancCs"|||j}|d||jS)z Binomial variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray variance = mu/n * (1 - mu/n) * self.n r)r'r"rrr&rrr r szBinomial.__call__cCs dd|S)r rrrrrrr r s zBinomial.derivN)rr rrrrr'r r rrrr r!s   r!zY The binomial variance function for n = 1 Notes ----- This is an alias of Binomial(n=1) c@r ) NegativeBinomiala  Negative binomial variance function Parameters ---------- alpha : float The ancillary parameter for the negative binomial variance function. `alpha` is assumed to be nonstochastic. The default is 1. Methods ------- call Returns the negative binomial variance Notes ----- Formulas : V(mu) = mu + alpha*mu**2 Alias for NegativeBinomial: nbinom = NegativeBinomial() A private method _clean trims the data by machine epsilon so that p is in (0,inf) rcCrr)alpha)rr+rrr rrzNegativeBinomial.__init__cCst|ttjSr)rr#r$infr%rrr r'szNegativeBinomial._cleancCs||}||j|dS)z Negative binomial variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray variance = mu + alpha*mu**2 rr'r+r(rrr r s zNegativeBinomial.__call__cCs||}dd|j|S)zH Derivative of the negative binomial variance function. rrr-r(rrr r s zNegativeBinomial.derivNrr)rrrr r*s   r*zb Negative Binomial variance function. Notes ----- This is an alias of NegativeBinomial(alpha=1.) )rZnumpyrZfinfofloatZepsr$rZconstantrrZ mu_squaredZmu_cubedr!Zbinaryr*Znbinomrrrr s& -9   = <