U mdg @sLdZddlZddlmZmZdZdRddZdSdd 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)TuDAsymmetric 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 st|r|nt||d}t|t|krt|dkrXt|dddf}|}dkrx|d}q|}n`dkrttt|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. Ncs(g|] }|dddfqSN.0xibwZkfuncsampleweightsr e/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/statsmodels/nonparametric/kernels_asymmetric.py |sz#pdf_kernel_asym..) callablekernel_dict_pdfnpsizelenasarraymeanones array_split concatenate) xrr kernel_typer batch_sizepdfipdfknx_splitr r rpdf_kernel_asym?s($      r%c st|r|nt||d}t|t|krt|dkrXt|dddf}|}dkrx|d}q|}n`dkrttt|t}t||} t|| } t fdd| 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. rrNrcs(g|] }|dddfqSrr r r r rrsz#cdf_kernel_asym..) rkernel_dict_cdfrrrrrrrr) rrrrrrcdfiZcdfr"r#r$r r rcdf_kernel_asyms($      r(cCs$tj|||dd||dSNr)rbetar!rrrr r rkernel_pdf_betasr,u Beta kernel for density, pdf, estimation. {doc_params} References ---------- .. [1] Bouezmarni, Taoufik, and Olivier Scaillet. 2005. “Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data.” Econometric Theory 21 (2): 390–412. .. [2] Chen, Song Xi. 1999. “Beta Kernel Estimators for Density Functions.” Computational Statistics & Data Analysis 31 (2): 131–45. https://doi.org/10.1016/S0167-9473(99)00010-9. ) doc_paramscCs$tj|||dd||dSr))rr*sfr+r r rkernel_cdf_betasr/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. c Csd|dd}d|dd|dd}t|dkr|d|kr~|t||d||}tj||d||}nh|dd|krd|}|t||d||}tj||||}ntj|||d||}n||}d||} |d|k} || }|t||d|||| <|dd|k} d|| }|t||d||| | <tj||| }|SNg@g@r)rrsqrtrr*r! rrrZa1Za2ar!Zx_alphar*Zmask_lowZmask_uppr r rkernel_pdf_beta2s*   " "r8u- 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 Csd|dd}d|dd|dd}t|dkr|d|kr~|t||d||}tj||d||}nh|dd|krd|}|t||d||}tj||||}ntj|||d||}n||}d||} |d|k} || }|t||d|||| <|dd|k} d|| }|t||d||| | <tj||| }|Sr0)rrr4rr*r.r5r r rkernel_cdf_beta2's*   " "r9u" 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. cCstjj|||d|d}|SNrscalergammar!)rrrr r r rkernel_pdf_gamma]sr?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. cCstjj|||d|d}|Sr:rr>r.)rrrr'r r rkernel_cdf_gammausrAu= 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. cCstjj||||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. r;r=r+r r r_kernel_pdf_gammas rBcCstjj||||dS)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. r;r@r+r r r_kernel_cdf_gammas rCcCstt|dkr6|d|kr,||dd}q^||}n(||}|d|k}||dd||<tjj|||d}|SNrr1r;)rrrr>r!rrrr6maskr!r r rkernel_pdf_gamma2s   rGuF 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. cCstt|dkr6|d|kr,||dd}q^||}n(||}|d|k}||dd||<tjj|||d}|SrD)rrrr>r.rEr r rkernel_cdf_gamma2s   rHu< 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. cCstjj|d|d||dSr:)rinvgammar!r+r r rkernel_pdf_invgammasrJu 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. cCstjj|d|d||dSr:)rrIr.r+r r rkernel_cdf_invgammasrKu_ 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. cCs"|}d|}tjj||||dSr:)rinvgaussr!rrrmZlamr r rkernel_pdf_invgausssrOuZ 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 rr1r)rr4piexprrrrr!r r rkernel_pdf_invgauss_'s(rTcCs"|}d|}tjj||||dSr:)rrLr.rMr r rkernel_cdf_invgauss1srUuj 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. cCs.d||}d|}tjj|||d|dSr:)r recipinvgaussr!rMr r rkernel_pdf_recipinvgaussFs rWue 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 rr1)rr4rQrRrSr r rkernel_pdf_recipinvgauss_^s $ rXcCs.d||}d|}tjj|||d|dSr:)rrVr.rMr r rkernel_cdf_recipinvgaussjs rYu[ 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. cCstjj|||dSNr;)r fatiguelifer!r+r r r kernel_pdf_bssr\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. cCstjj|||dSrZ)rr[r.r+r r r kernel_cdf_bssr]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. cCs*tdtd|}tjj|||dSNr2rr;)rr4logrlognormr!rrrZbw_r r rkernel_pdf_lognorms rbu 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. cCs*tdtd|}tjj|||dSr^)rr4r_rr`r.rar r rkernel_cdf_lognorms rcu 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 rr1r)rr_r4rQrRr)rrrtermr!r r rkernel_pdf_lognorm_s "rfcCs$tjj|d||td|dSr:)r weibull_minr!rr>r+r r rkernel_pdf_weibullsrhu\ Weibull kernel for density, pdf, estimation. Based on cdf kernel by Mombeni et al. (2019) {doc_params} References ---------- .. [1] Mombeni, Habib Allah, B Masouri, and Mohammad Reza Akhoond. 2019. “Asymmetric Kernels for Boundary Modification in Distribution Function Estimation.” REVSTAT, 1–27. cCs$tjj|d||td|dSr:)rrgr.rr>r+r r rkernel_cdf_weibullsriu: 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*Zbeta2bsr>Zgamma2rIrLr`rVZweibull)Nr)Nr)%__doc__numpyrZscipyrrr-r%r(r,formatr/r8r9r?rArBrCrGrHrJrKrOrTrUrWrXrYr\r]rbrcrfrhrir&rr r r rs+ C C%%