M/Phg 8dZddlZddlmZmZdZd7dZd7dZdZ d e e _d Z d e e _d Z d e e _dZ d e e _dZd e e_dZd e e_dZdZdZd e e_dZd e e_dZd e e_dZd e e_dZd e e_d!Zd"Zd# e e_d$Zd% e e_d&Zd'Zd( e e_d)Zd* e e_d+Zd, e e_d-Zd. e e_d/Zd0 e e_d1Z d2Z!d3 e e!_d4Z"d5 e e"_e e eeeeeeee"d6 Z#e e eeeeeeee!d6 Z$dS)8uDAsymmetric 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| n t| |dz}tj|t z|kratj|dkrtj|dddf} |}|d}n|z}n1tjt t z |t z}t ||z} tj|| } tj  fd| 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. NcDg|]}|dddfzSN.0xibwkfuncsampleweightss l/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/nonparametric/kernels_asymmetric.py z#pdf_kernel_asym..{H111"$ %uR4[&"==G111) callablekernel_dict_pdfnpsizelenasarraymeanones array_split concatenate) xrr kernel_typer batch_sizepdfipdfknx_splitrs `` ` @rpdf_kernel_asymr*>UH - ,d"J wqzzCKK*,, 71::>> 1 aaag&AuQ## ?))B--CC.CC ?gc&kk**S[[8G #f++ % FFaK.A&&n1111111(/11122 Jrc t|r| n t| |dz}tj|t z|kratj|dkrtj|dddf} |}|d}n|z}n1tjt t z |t z}t ||z} tj|| } tj  fd| D}|S)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 cDg|]}|dddfzSr r r s rrz#cdf_kernel_asym..rr) rkernel_dict_cdfrrrrrrr r!) r"rrr#rr$cdficdfr'r(r)rs `` ` @rcdf_kernel_asymr1r+rcbtj|||z dzd|z |z dzSNr)rbetar&r"rrs rkernel_pdf_betar6s/ :>>&!b&1*q1ulQ.> ? ??ru Beta kernel for density, pdf, estimation. {doc_params} References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 1999. “Beta Kernel Estimators for Density Functions.” Computational Statistics & Data Analysis 31 (2): 131–45. https://doi.org/10.1016/S0167-9473(99)00010-9. ) doc_paramscbtj|||z dzd|z |z dzSr3)rr4sfr5s rkernel_cdf_betar:s/ :==R!a!er\A-= > >>ru# Beta kernel for cumulative distribution, cdf, estimation. {doc_params} References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 1999. “Beta Kernel Estimators for Density Functions.” Computational Statistics & Data Analysis 31 (2): 131–45. https://doi.org/10.1016/S0167-9473(99)00010-9. cjd|dzzdz}d|dzzd|dzzzdz}tj|dkr|d|zkrL|tj||dzz ||z z z }tj||d|z |z }n&|dd|zz krMd|z }|tj||dzz ||z z z }tj|||z |}ntj|||z d|z |z }n||z }d|z |z } |d|zk} || }|tj||dzz ||z z z || <|dd|zz k} d|| z }|tj||dzz ||z z z | | <tj||| }|SNg@g@r)rrsqrtrr4r& r"rra1a2ar&x_alphar4mask_lowmask_upps rkernel_pdf_beta2rIs RUSB RUQQY  %B wqzzQ q2v::RWR!Q$YR/000A*..QUbL99CC !a"f*  QBRWR"a%Z"r'1222A*..R33CC*..R!a%2>>CCBA|q2v: x[rwrBEzBG';<<<hAF # 8_bgb2q5j27&:;;;XjnnVUD11 Jru- 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. cjd|dzzdz}d|dzzd|dzzzdz}tj|dkr|d|zkrL|tj||dzz ||z z z }tj||d|z |z }n&|dd|zz krMd|z }|tj||dzz ||z z z }tj|||z |}ntj|||z d|z |z }n||z }d|z |z } |d|zk} || }|tj||dzz ||z z z || <|dd|zz k} d|| z }|tj||dzz ||z z z | | <tj||| }|Sr<)rrr@rr4r9rAs rkernel_cdf_beta2rK&s RUSB RUQQY  %B wqzzQ q2v::RWR!Q$YR/000A*--AER<88CC !a"f*  QBRWR"a%Z"r'1222A*--B22CC*--BQ" ==CCBA|q2v: x[rwrBEzBG';<<<hAF # 8_bgb2q5j27&:;;;XjmmFE400 Jru" 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. cVtj|||z dz|}|SNrscalergammar&)r"rrr%s rkernel_pdf_gammarR\s( ;??61r6A:R? 8 8D Kru- 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. cVtj|||z dz|}|SrMrrQr9)r"rrr/s rkernel_cdf_gammarUts* ;>>&!b&1*B> 7 7D Kru= 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. cLtj|||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. rNrPr5s r_kernel_pdf_gammarWs" ;??61r6? 4 44rcLtj|||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. rNrTr5s r_kernel_cdf_gammarYs" ;>>&!b&> 3 33rctj|dkr|d|zkr ||z dzdz}n%||z }n||z }|d|zk}||dzdz||<tj|||}|SNrr=rN)rrrrQr&r"rrrDmaskr&s rkernel_pdf_gamma2r^s wqzzQ q2v::R! aAABAA F1r6zD'1*q.$ +//&!2/ . .C JruF 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|dkr|d|zkr ||z dzdz}n%||z }n||z }|d|zk}||dzdz||<tj|||}|Sr[)rrrrQr9r\s rkernel_cdf_gamma2r`s wqzzQ q2v::R! aAABAA F1r6zD'1*q.$ +..". - -C Jru< 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. cXtj|d|z dz||z SrM)rinvgammar&r5s rkernel_pdf_invgammarcs+ >  fa"fqjB  ? ??ru 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. cXtj|d|z dz||z SrM)rrbr9r5s rkernel_cdf_invgammares+ >  VQVaZq2v  > >>ru_ 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 }tj|||z |SrM)rinvgaussr&r"rrmlams rkernel_pdf_invgaussrks1 A b&C >  fa#gS  9 99ruZ 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}|dS)zJInverse gaussian kernel density, explicit formula. Scaillet 2004 rr=r )rr@piexprr"rrr&s rkernel_pdf_invgauss_rq&sq rwq25y2~ 122 2 6#R!$ QV(CD E E FC 88B<<rcZ|}d|z }tj|||z |SrM)rrgr9rhs rkernel_cdf_invgaussrs0s1 A b&C >  VQWC  8 88ruj 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 }tj|||z d|z SrM)r recipinvgaussr&rhs rkernel_pdf_recipinvgaussrvEs@ QV A b&C   " "61s7!c' " B BBrue 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 rr=)rr@rnrorps rkernel_pdf_recipinvgauss_rx]sw rwq25y2~.// / 6QV*B'&0AF;a?r6V#$ % % %C Jrcld||z z }d|z }tj|||z d|z SrM)rrur9rhs rkernel_cdf_recipinvgaussrzis@ QV A b&C   ! !&!c'S ! A AAru[ 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. cFtj|||SNrN)r fatiguelifer&r5s r kernel_pdf_bsr~s   1 5 55ruZ 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. cFtj|||Sr|)rr}r9r5s r kernel_cdf_bsrs    !  4 44ru 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}tj|||SNr>rrN)rr@logrlognormr&r"rrbw_s rkernel_pdf_lognormrs@ '!BF1R4LL. ! !C =  VS  2 22ru 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}tj|||Sr)rr@rrrr9rs rkernel_cdf_lognormrs@ '!BF1R4LL. ! !C =  FCq  1 11ru 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. c4dtjd|zz}dtj|tjzz |z tjtj|tj|z dz |z z}|dS)z]Log-normal kernel for density, pdf, estimation, explicit formula. Jin, Kawczak 2003 rr=r )rrr@rnror)r"rrtermr&s rkernel_pdf_lognorm_rs} rva"f~~ D rwtbe|$$ $v - 6RVAYY/!33d: ; ; rs))V  ( @@@@F@@@@F@@@  *%%"???  *%%""""J *%%""""J *%%"  *%%$ *%%$ 5 5 5 4 4 4" *%%$" *%%$@@@  *%%???  *%%:::  *%%999  *%%CCC $ *%%    BBB $ *%% 666  *%%555  *%% 3 3 3 *%%" 2 2 2 *%%"BBB  *%%AAA  *%%"    ##!-!      ##!-!  r