o 0Gfg @sLdZddlZddlmZmZdZdRddZdRdd Zd d Z d j ed e _ddZ dj ed e _ddZ dj ed e _ddZ dj ed e _ddZdj ed e_ddZdj ed e_ddZdd Zd!d"Zd#j ed e_d$d%Zd&j ed e_d'd(Zd)j ed e_d*d+Zd,j ed e_d-d.Zd/j ed e_d0d1Zd2d3Zd4j ed e_d5d6Zd7j ed e_d8d9Zd:d;ZdZd?j ed e_d@dAZdBj ed e_dCdDZdEj ed e_dFdGZdHj ed e_dIdJZ dKdLZ!dMj ed e!_dNdOZ"dPj ed e"_e e eeeeeeee"dQ Z#e e eeeeeeee!dQ Z$dS)SuDAsymmetric kernels for R+ and unit interval References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 1999. “Beta Kernel Estimators for Density Functions.” Computational Statistics & Data Analysis 31 (2): 131–45. https://doi.org/10.1016/S0167-9473(99)00010-9. .. [3] Chen, Song Xi. 2000. “Probability Density Function Estimation Using Gamma Kernels.” Annals of the Institute of Statistical Mathematics 52 (3): 471–80. https://doi.org/10.1023/A:1004165218295. .. [4] Jin, Xiaodong, and Janusz Kawczak. 2003. “Birnbaum-Saunders and Lognormal Kernel Estimators for Modelling Durations in High Frequency Financial Data.” Annals of Economics and Finance 4: 103–24. .. [5] Micheaux, Pierre Lafaye de, and Frédéric Ouimet. 2020. “A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions,” November. https://arxiv.org/abs/2011.14893v1. .. [6] Mombeni, Habib Allah, B Masouri, and Mohammad Reza Akhoond. 2019. “Asymmetric Kernels for Boundary Modification in Distribution Function Estimation.” REVSTAT, 1–27. .. [7] Scaillet, O. 2004. “Density Estimation Using Inverse and Reciprocal Inverse Gaussian Kernels.” Journal of Nonparametric Statistics 16 (1–2): 217–26. https://doi.org/10.1080/10485250310001624819. Created on Mon Mar 8 11:12:24 2021 Author: Josef Perktold License: BSD-3 N)specialstatsa[Parameters ---------- x : array_like, float Points for which density is evaluated. ``x`` can be scalar or 1-dim. sample : ndarray, 1-d Sample from which kde is computed. bw : float Bandwidth parameter, there is currently no default value for it. Returns ------- Components for kernel estimation c t|r|nt||d}t|t|krCt|dkr,t|dddf}|}dur=|d}|S|}|SdurRttt|t}t||} t|| } t fdd| D}|S)acDensity estimate based on asymmetric kernel. Parameters ---------- x : array_like, float Points for which density is evaluated. ``x`` can be scalar or 1-dim. sample : ndarray, 1-d Sample from which kernel estimate is computed. bw : float Bandwidth parameter, there is currently no default value for it. kernel_type : str or callable Kernel name or kernel function. Currently supported kernel names are "beta", "beta2", "gamma", "gamma2", "bs", "invgamma", "invgauss", "lognorm", "recipinvgauss" and "weibull". weights : None or ndarray If weights is not None, then kernel for sample points are weighted by it. No weights corresponds to uniform weighting of each component with 1 / nobs, where nobs is the size of `sample`. batch_size : float If x is an 1-dim array, then points can be evaluated in vectorized form. To limit the amount of memory, a loop can work in batches. The number of batches is determined so that the intermediate array sizes are limited by ``np.size(batch) * len(sample) < batch_size * 1000``. Default is to have at most 10000 elements in intermediate arrays. Returns ------- pdf : float or ndarray Estimate of pdf at points x. ``pdf`` has the same size or shape as x. Nc(g|]}|dddfqSN.0ZxibwZkfuncsampleweightsr Llib/python3.10/site-packages/statsmodels/nonparametric/kernels_asymmetric.py { z#pdf_kernel_asym..) callablekernel_dict_pdfnpsizelenasarraymeanones array_split concatenate) xrr kernel_typer batch_sizepdfipdfknx_splitr rrpdf_kernel_asym>,$      r'c r)avEstimate of cumulative distribution based on asymmetric kernel. Parameters ---------- x : array_like, float Points for which density is evaluated. ``x`` can be scalar or 1-dim. sample : ndarray, 1-d Sample from which kernel estimate is computed. bw : float Bandwidth parameter, there is currently no default value for it. kernel_type : str or callable Kernel name or kernel function. Currently supported kernel names are "beta", "beta2", "gamma", "gamma2", "bs", "invgamma", "invgauss", "lognorm", "recipinvgauss" and "weibull". weights : None or ndarray If weights is not None, then kernel for sample points are weighted by it. No weights corresponds to uniform weighting of each component with 1 / nobs, where nobs is the size of `sample`. batch_size : float If x is an 1-dim array, then points can be evaluated in vectorized form. To limit the amount of memory, a loop can work in batches. The number of batches is determined so that the intermediate array sizes are limited by ``np.size(batch) * len(sample) < batch_size * 1000``. Default is to have at most 10000 elements in intermediate arrays. Returns ------- cdf : float or ndarray Estimate of cdf at points x. ``cdf`` has the same size or shape as x. rrNrcr r r r rr rrrz#cdf_kernel_asym..) rkernel_dict_cdfrrrrrrrr) rrrr rr!cdfiZcdfr$r%r&r rrcdf_kernel_asymr(r+cC$tj|||dd||dSNr)rbetar#rrrr r rkernel_pdf_beta$r0u Beta kernel for density, pdf, estimation. {doc_params} References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 1999. “Beta Kernel Estimators for Density Functions.” Computational Statistics & Data Analysis 31 (2): 131–45. https://doi.org/10.1016/S0167-9473(99)00010-9. ) doc_paramscCr,r-)rr.sfr/r r rkernel_cdf_betar1r4u# Beta kernel for cumulative distribution, cdf, estimation. {doc_params} References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 1999. “Beta Kernel Estimators for Density Functions.” Computational Statistics & Data Analysis 31 (2): 131–45. https://doi.org/10.1016/S0167-9473(99)00010-9. c Cd|dd}d|dd|dd}t|dkrw|d|kr@|t||d||}tj||d||}|S|dd|krgd|}|t||d||}tj||||}|Stj|||d||}|S||}d||} |d|k} || }|t||d|||| <|dd|k} d|| }|t||d||| | <tj||| }|SNg@g@r)rrsqrtrr.r# rrrZa1Za2ar#Zx_Zalphar.Zmask_lowZmask_uppr r rkernel_pdf_beta2s0   " "r=u- Beta kernel for density, pdf, estimation with boundary corrections. {doc_params} References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 1999. “Beta Kernel Estimators for Density Functions.” Computational Statistics & Data Analysis 31 (2): 131–45. https://doi.org/10.1016/S0167-9473(99)00010-9. c Cr5r6)rrr:rr.r3r;r r rkernel_cdf_beta2&s0   " "r>u" Beta kernel for cdf estimation with boundary correction. {doc_params} References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 1999. “Beta Kernel Estimators for Density Functions.” Computational Statistics & Data Analysis 31 (2): 131–45. https://doi.org/10.1016/S0167-9473(99)00010-9. cCtjj|||d|d}|SNrZscalergammar#)rrrr"r r rkernel_pdf_gamma\srDu- Gamma kernel for density, pdf, estimation. {doc_params} References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 2000. “Probability Density Function Estimation Using Gamma Krnels.” Annals of the Institute of Statistical Mathematics 52 (3): 471–80. https://doi.org/10.1023/A:1004165218295. cCr?r@rrCr3)rrrr*r r rkernel_cdf_gammatsrFu= Gamma kernel for cumulative distribution, cdf, estimation. {doc_params} References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 2000. “Probability Density Function Estimation Using Gamma Krnels.” Annals of the Institute of Statistical Mathematics 52 (3): 471–80. https://doi.org/10.1023/A:1004165218295. cCtjj||||dS)zGamma kernel for pdf, without boundary corrected part. drops `+ 1` in shape parameter It should be possible to use this if probability in neighborhood of zero boundary is small. rArBr/r r r_kernel_pdf_gamma rHcCrG)zGamma kernel for cdf, without boundary corrected part. drops `+ 1` in shape parameter It should be possible to use this if probability in neighborhood of zero boundary is small. rArEr/r r r_kernel_cdf_gammarIrJcCtt|dkr|d|kr||dd}n||}n||}|d|k}||dd||<tjj|||d}|SNrr7rA)rrrrCr#rrrr<maskr#r r rkernel_pdf_gamma2   rOuF Gamma kernel for density, pdf, estimation with boundary correction. {doc_params} References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 2000. “Probability Density Function Estimation Using Gamma Krnels.” Annals of the Institute of Statistical Mathematics 52 (3): 471–80. https://doi.org/10.1023/A:1004165218295. cCrKrL)rrrrCr3rMr r rkernel_cdf_gamma2rPrQu< Gamma kernel for cdf estimation with boundary correction. {doc_params} References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 2000. “Probability Density Function Estimation Using Gamma Krnels.” Annals of the Institute of Statistical Mathematics 52 (3): 471–80. https://doi.org/10.1023/A:1004165218295. cCtjj|d|d||dSr@)rinvgammar#r/r r rkernel_pdf_invgammarTu Inverse gamma kernel for density, pdf, estimation. Based on cdf kernel by Micheaux and Ouimet (2020) {doc_params} References ---------- .. [1] Micheaux, Pierre Lafaye de, and Frédéric Ouimet. 2020. “A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions,” November. https://arxiv.org/abs/2011.14893v1. cCrRr@)rrSr3r/r r rkernel_cdf_invgammarUrVu_ Inverse gamma kernel for cumulative distribution, cdf, estimation. {doc_params} References ---------- .. [1] Micheaux, Pierre Lafaye de, and Frédéric Ouimet. 2020. “A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions,” November. https://arxiv.org/abs/2011.14893v1. cC"|}d|}tjj||||dSr@)rinvgaussr#rrrmZlamr r rkernel_pdf_invgaussr[uZ Inverse gaussian kernel for density, pdf, estimation. {doc_params} References ---------- .. [1] Scaillet, O. 2004. “Density Estimation Using Inverse and Reciprocal Inverse Gaussian Kernels.” Journal of Nonparametric Statistics 16 (1–2): 217–26. https://doi.org/10.1080/10485250310001624819. cCsTdtdtj||dtdd||||d||}|dS)zJInverse gaussian kernel density, explicit formula. Scaillet 2004 rr7r)rr:piexprrrrr#r r rkernel_pdf_invgauss_&s( racCrWr@)rrXr3rYr r rkernel_cdf_invgauss0r\rbuj Inverse gaussian kernel for cumulative distribution, cdf, estimation. {doc_params} References ---------- .. [1] Scaillet, O. 2004. “Density Estimation Using Inverse and Reciprocal Inverse Gaussian Kernels.” Journal of Nonparametric Statistics 16 (1–2): 217–26. https://doi.org/10.1080/10485250310001624819. cC.d||}d|}tjj|||d|dSr@)r recipinvgaussr#rYr r rkernel_pdf_recipinvgaussE reue Reciprocal inverse gaussian kernel for density, pdf, estimation. {doc_params} References ---------- .. [1] Scaillet, O. 2004. “Density Estimation Using Inverse and Reciprocal Inverse Gaussian Kernels.” Journal of Nonparametric Statistics 16 (1–2): 217–26. https://doi.org/10.1080/10485250310001624819. cCsTdtdtj||t|| d||||d|||}|S)zUReciprocal inverse gaussian kernel density, explicit formula. Scaillet 2004 rr7)rr:r^r_r`r r rkernel_pdf_recipinvgauss_]s $ rgcCrcr@)rrdr3rYr r rkernel_cdf_recipinvgaussirfrhu[ Reciprocal inverse gaussian kernel for cdf estimation. {doc_params} References ---------- .. [1] Scaillet, O. 2004. “Density Estimation Using Inverse and Reciprocal Inverse Gaussian Kernels.” Journal of Nonparametric Statistics 16 (1–2): 217–26. https://doi.org/10.1080/10485250310001624819. cCtjj|||dSNrA)r fatiguelifer#r/r r r kernel_pdf_bsrluZ Birnbaum Saunders (normal) kernel for density, pdf, estimation. {doc_params} References ---------- .. [1] Jin, Xiaodong, and Janusz Kawczak. 2003. “Birnbaum-Saunders and Lognormal Kernel Estimators for Modelling Durations in High Frequency Financial Data.” Annals of Economics and Finance 4: 103–24. cCrirj)rrkr3r/r r r kernel_cdf_bsrmrnu Birnbaum Saunders (normal) kernel for cdf estimation. {doc_params} References ---------- .. [1] Jin, Xiaodong, and Janusz Kawczak. 2003. “Birnbaum-Saunders and Lognormal Kernel Estimators for Modelling Durations in High Frequency Financial Data.” Annals of Economics and Finance 4: 103–24. .. [2] Mombeni, Habib Allah, B Masouri, and Mohammad Reza Akhoond. 2019. “Asymmetric Kernels for Boundary Modification in Distribution Function Estimation.” REVSTAT, 1–27. cC*tdtd|}tjj|||dSNr8rrA)rr:logrlognormr#rrrZbw_r r rkernel_pdf_lognorm rtu Log-normal kernel for density, pdf, estimation. {doc_params} Notes ----- Warning: parameterization of bandwidth will likely be changed References ---------- .. [1] Jin, Xiaodong, and Janusz Kawczak. 2003. “Birnbaum-Saunders and Lognormal Kernel Estimators for Modelling Durations in High Frequency Financial Data.” Annals of Economics and Finance 4: 103–24. cCrorp)rr:rqrrrr3rsr r rkernel_cdf_lognormrurvu Log-normal kernel for cumulative distribution, cdf, estimation. {doc_params} Notes ----- Warning: parameterization of bandwidth will likely be changed References ---------- .. [1] Jin, Xiaodong, and Janusz Kawczak. 2003. “Birnbaum-Saunders and Lognormal Kernel Estimators for Modelling Durations in High Frequency Financial Data.” Annals of Economics and Finance 4: 103–24. cCsXdtd|}dt|tj|tt|t|d |}|dS)z]Log-normal kernel for density, pdf, estimation, explicit formula. Jin, Kawczak 2003 rr7r)rrqr:r^r_r)rrrZtermr#r r rkernel_pdf_lognorm_s " rxcC$tjj|d||td|dSr@)r weibull_minr#rrCr/r r rkernel_pdf_weibullr{u\ Weibull kernel for density, pdf, estimation. Based on cdf kernel by Mombeni et al. (2019) {doc_params} References ---------- .. [1] Mombeni, Habib Allah, B Masouri, and Mohammad Reza Akhoond. 2019. “Asymmetric Kernels for Boundary Modification in Distribution Function Estimation.” REVSTAT, 1–27. cCryr@)rrzr3rrCr/r r rkernel_cdf_weibullr|r}u: Weibull kernel for cumulative distribution, cdf, estimation. {doc_params} References ---------- .. [1] Mombeni, Habib Allah, B Masouri, and Mohammad Reza Akhoond. 2019. “Asymmetric Kernels for Boundary Modification in Distribution Function Estimation.” REVSTAT, 1–27. ) r.Zbeta2bsrCZgamma2rSrXrrrdZweibull)Nr)%__doc__ZnumpyrZscipyrrr2r'r+r0formatr4r=r>rDrFrHrJrOrQrTrVr[rarbrergrhrlrnrtrvrxr{r}r)rr r r rs+  CC%%