!gg dZddlZddlmZmZdZd6dZd6dZdZ dje e _d Z d je e _d Z d je e _dZ dje e _dZdje e_dZdje e_dZdZdZdje e_dZdje e_dZdje e_dZdje e_dZdje e_d Zd!Zd"je e_d#Zd$je e_d%Zd&Zd'je e_d(Zd)je e_d*Zd+je e_d,Zd-je e_d.Zd/je e_d0Z d1Z!d2je e!_d3Z"d4je e"_e e eeeeeeee"d5 Z#e e eeeeeeee!d5 Z$y)7uDAsymmetric 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 estimationc jt|r|}n t|}|dz}tj|t |z|krZtj|dkDrtj |dddf}||||}||j d}|S||z}|S|*tjt |t |z }|t |z} t || z} tj|| } tj| D cgc]} || dddf|||zc} }|Scc} w)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. N) callablekernel_dict_pdfnpsizelenasarraymeanones array_split concatenate) xsamplebw kernel_typeweights batch_sizekfuncpdfipdfknx_splitxis i/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/nonparametric/kernels_asymmetric.pypdf_kernel_asymr!>0H  ,d"J wwqzCK*, 771:> 1 ag&AQ# ?))B-C J.C J ?ggc&k*S[8G #f+ % FaK..A&nn(/1"$ %R4[&"=G12 J1 D0c jt|r|}n t|}|dz}tj|t |z|krZtj|dkDrtj |dddf}||||}||j d}|S||z}|S|*tjt |t |z }|t |z} t || z} tj|| } tj| D cgc]} || dddf|||zc} }|Scc} w)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. rrNr) r kernel_dict_cdfr r r rrrrr) rrrrrrrcdficdfrrrrs r cdf_kernel_asymr(r"r#cbtjj|||z dzd|z |z dzSNr)rbetarrrrs r kernel_pdf_betar-s. ::>>&!b&1*q1ulQ.> ??u 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_paramscbtjj|||z dzd|z |z dzSr*)rr+sfr,s r kernel_cdf_betar2s. ::==R!a!er\A-= >>r.u# 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. cbd|dzzdz}d|dzzd|dzzzdz}tj|dk(r|d|zkrM|tj||dzz ||z z z }tjj ||d|z |z }|S|dd|zz kDrOd|z }|tj||dzz ||z z z }tjj |||z |}|Stjj |||z d|z |z }|S||z }d|z |z } |d|zk} || }|tj||dzz ||z z z || <|dd|zz kD} d|| z }|tj||dzz ||z z z | | <tjj ||| }|SNg@g@r)r r sqrtrr+r rrra1a2arx_alphar+mask_lowmask_upps r kernel_pdf_beta2rAs RUSB RUQQY  %B wwqzQ q2v:RWWR!Q$YR/00A**..QUbL9C* J)!a"f* QBRWWR"a%Z"r'122A**..R3C" J**..R!a%2>C JBA|q2v: x[rwwrBEzBG';<<hAF # 8_bggb2q5j27&:;;XjjnnVUD1 Jr.u- Beta kernel for density, pdf, estimation with boundary corrections. {doc_params} References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 1999. “Beta Kernel Estimators for Density Functions.” Computational Statistics & Data Analysis 31 (2): 131–45. https://doi.org/10.1016/S0167-9473(99)00010-9. cbd|dzzdz}d|dzzd|dzzzdz}tj|dk(r|d|zkrM|tj||dzz ||z z z }tjj ||d|z |z }|S|dd|zz kDrOd|z }|tj||dzz ||z z z }tjj |||z |}|Stjj |||z d|z |z }|S||z }d|z |z } |d|zk} || }|tj||dzz ||z z z || <|dd|zz kD} d|| z }|tj||dzz ||z z z | | <tjj ||| }|Sr4)r r r8rr+r1r9s r kernel_cdf_beta2rC&s RUSB RUQQY  %B wwqzQ q2v:RWWR!Q$YR/00A**--AER<8C* J)!a"f* QBRWWR"a%Z"r'122A**--B2C" J**--BQ" =C JBA|q2v: x[rwwrBEzBG';<<hAF # 8_bggb2q5j27&:;;XjjmmFE40 Jr.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. cVtjj|||z dz|}|SNrscalergammar)rrrrs r kernel_pdf_gammarJ\s' ;;??61r6A:R? 8D Kr.u- 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. cVtjj|||z dz|}|SrErrIr1)rrrr&s r kernel_cdf_gammarMts) ;;>>&!b&1*B> 7D Kr.u= 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. cLtjj|||z |S)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. rFrHr,s r _kernel_pdf_gammarOs! ;;??61r6? 44r.cLtjj|||z |S)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. rFrLr,s r _kernel_cdf_gammarQs! ;;>>&!b&> 33r.ctj|dk(r|d|zkr ||z dzdz}n!||z }n||z }|d|zk}||dzdz||<tjj |||}|SNrr5rF)r r rrIrrrrr<maskrs r kernel_pdf_gamma2rVs~ wwqzQ q2v:R! aABA F1r6zD'1*q.$ ++//&!2/ .C Jr.uF 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. ctj|dk(r|d|zkr ||z dzdz}n!||z }n||z }|d|zk}||dzdz||<tjj |||}|SrS)r r rrIr1rTs r kernel_cdf_gamma2rXs~ wwqzQ q2v:R! aABA F1r6zD'1*q.$ ++..". -C Jr.u< 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. cXtjj|d|z dz||z SrE)rinvgammarr,s r kernel_pdf_invgammar[s* >>  fa"fqjB  ??r.u 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. cXtjj|d|z dz||z SrE)rrZr1r,s r kernel_cdf_invgammar]s* >>  VQVaZq2v  >>r.u_ 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. cZ|}d|z }tjj|||z |SrE)rinvgaussrrrrmlams r kernel_pdf_invgaussrcs0 A b&C >>  fa#gS  99r.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. cdtjdtjz|z|dzzz tjdd|z|zz ||z dz ||z zzz}|j dS)zJInverse gaussian kernel density, explicit formula. Scaillet 2004 rr5r)r r8piexprrrrrs r kernel_pdf_invgauss_ri&so rwwq255y2~ 12 2 66#R!$ QV(CD E FC 88B<r.cZ|}d|z }tjj|||z |SrE)rr_r1r`s r kernel_cdf_invgaussrk0s0 A b&C >>  VQWC  88r.uj 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. cld||z z }d|z }tjj|||z d|z SrE)r recipinvgaussrr`s r kernel_pdf_recipinvgaussrnEs@ QV A b&C    " "61s7!c' " BBr.ue 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. cdtjdtjz|z|zz tj||z d|zz |z||z z dz ||z |z zz}|S)zUReciprocal inverse gaussian kernel density, explicit formula. Scaillet 2004 rr5)r r8rfrgrhs r kernel_pdf_recipinvgauss_rp]su rwwq255y2~./ / 66QV*B'&0AF;a?r6V#$ % %C Jr.cld||z z }d|z }tjj|||z d|z SrE)rrmr1r`s r kernel_cdf_recipinvgaussrris@ QV A b&C    ! !&!c'S ! AAr.u[ 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. cFtjj|||SNrF)r fatigueliferr,s r kernel_pdf_bsrvs    1 55r.uZ 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. cFtjj|||Srt)rrur1r,s r kernel_cdf_bsrxs     !  44r.u 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. ctjdtjd|zz}tjj |||SNr6rrF)r r8logrlognormrrrrbw_s r kernel_pdf_lognormrs> ''!BFF1R4L. !C ==  VS  22r.u 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. ctjdtjd|zz}tjj |||Srz)r r8r{rr|r1r}s r kernel_cdf_lognormrs> ''!BFF1R4L. !C ==  FCq  11r.u 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. c>dtjd|zz}dtj|tjzz |z tjtj|tj|z dz |z z}|j dS)z]Log-normal kernel for density, pdf, estimation, explicit formula. Jin, Kawczak 2003 rr5r)r r{r8rfrgr)rrrtermrs r kernel_pdf_lognorm_rs{ rvva"f~ D rwwtbee|$ $v - 66RVVAY/!33d: ; rs)V  ( @F@F@  *%"?  *%""J *%""J *%"  *%$ *%$ 5 4" *%$" *%$@  *%?  *%:  *%9  *%C $ *%  B $ *% 6  *%5  *% 3 *%" 2 *%"B  *%A  *%"    ##!-!     ##!-! r.