Source code for statsmodels.nonparametric.kernels_asymmetric

"""Asymmetric 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

"""

import numpy as np
from scipy import special, stats

doc_params = """\
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"""


[docs] def pdf_kernel_asym(x, sample, bw, kernel_type, weights=None, batch_size=10): """Density 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. """ if callable(kernel_type): kfunc = kernel_type else: kfunc = kernel_dict_pdf[kernel_type] batch_size = batch_size * 1000 if np.size(x) * len(sample) < batch_size: # no batch-loop if np.size(x) > 1: x = np.asarray(x)[:, None] pdfi = kfunc(x, sample, bw) if weights is None: pdf = pdfi.mean(-1) else: pdf = pdfi @ weights else: # batch, designed for 1-d x if weights is None: weights = np.ones(len(sample)) / len(sample) k = batch_size // len(sample) n = len(x) // k x_split = np.array_split(x, n) pdf = np.concatenate([(kfunc(xi[:, None], sample, bw) @ weights) for xi in x_split]) return pdf
[docs] def cdf_kernel_asym(x, sample, bw, kernel_type, weights=None, batch_size=10): """Estimate 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. """ if callable(kernel_type): kfunc = kernel_type else: kfunc = kernel_dict_cdf[kernel_type] batch_size = batch_size * 1000 if np.size(x) * len(sample) < batch_size: # no batch-loop if np.size(x) > 1: x = np.asarray(x)[:, None] cdfi = kfunc(x, sample, bw) if weights is None: cdf = cdfi.mean(-1) else: cdf = cdfi @ weights else: # batch, designed for 1-d x if weights is None: weights = np.ones(len(sample)) / len(sample) k = batch_size // len(sample) n = len(x) // k x_split = np.array_split(x, n) cdf = np.concatenate([(kfunc(xi[:, None], sample, bw) @ weights) for xi in x_split]) return cdf
[docs] def kernel_pdf_beta(x, sample, bw): # Beta kernel for density, pdf, estimation return stats.beta.pdf(sample, x / bw + 1, (1 - x) / bw + 1)
kernel_pdf_beta.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_cdf_beta(x, sample, bw): # Beta kernel for cumulative distribution, cdf, estimation return stats.beta.sf(sample, x / bw + 1, (1 - x) / bw + 1)
kernel_cdf_beta.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_pdf_beta2(x, sample, bw): # Beta kernel for density, pdf, estimation with boundary corrections # a = 2 * bw**2 + 2.5 - # np.sqrt(4 * bw**4 + 6 * bw**2 + 2.25 - x**2 - x / bw) # terms a1 and a2 are independent of x a1 = 2 * bw**2 + 2.5 a2 = 4 * bw**4 + 6 * bw**2 + 2.25 if np.size(x) == 1: # without vectorizing: if x < 2 * bw: a = a1 - np.sqrt(a2 - x**2 - x / bw) pdf = stats.beta.pdf(sample, a, (1 - x) / bw) elif x > (1 - 2 * bw): x_ = 1 - x a = a1 - np.sqrt(a2 - x_**2 - x_ / bw) pdf = stats.beta.pdf(sample, x / bw, a) else: pdf = stats.beta.pdf(sample, x / bw, (1 - x) / bw) else: alpha = x / bw beta = (1 - x) / bw mask_low = x < 2 * bw x_ = x[mask_low] alpha[mask_low] = a1 - np.sqrt(a2 - x_**2 - x_ / bw) mask_upp = x > (1 - 2 * bw) x_ = 1 - x[mask_upp] beta[mask_upp] = a1 - np.sqrt(a2 - x_**2 - x_ / bw) pdf = stats.beta.pdf(sample, alpha, beta) return pdf
kernel_pdf_beta2.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_cdf_beta2(x, sample, bw): # Beta kernel for cdf estimation with boundary correction # a = 2 * bw**2 + 2.5 - # np.sqrt(4 * bw**4 + 6 * bw**2 + 2.25 - x**2 - x / bw) # terms a1 and a2 are independent of x a1 = 2 * bw**2 + 2.5 a2 = 4 * bw**4 + 6 * bw**2 + 2.25 if np.size(x) == 1: # without vectorizing: if x < 2 * bw: a = a1 - np.sqrt(a2 - x**2 - x / bw) pdf = stats.beta.sf(sample, a, (1 - x) / bw) elif x > (1 - 2 * bw): x_ = 1 - x a = a1 - np.sqrt(a2 - x_**2 - x_ / bw) pdf = stats.beta.sf(sample, x / bw, a) else: pdf = stats.beta.sf(sample, x / bw, (1 - x) / bw) else: alpha = x / bw beta = (1 - x) / bw mask_low = x < 2 * bw x_ = x[mask_low] alpha[mask_low] = a1 - np.sqrt(a2 - x_**2 - x_ / bw) mask_upp = x > (1 - 2 * bw) x_ = 1 - x[mask_upp] beta[mask_upp] = a1 - np.sqrt(a2 - x_**2 - x_ / bw) pdf = stats.beta.sf(sample, alpha, beta) return pdf
kernel_cdf_beta2.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_pdf_gamma(x, sample, bw): # Gamma kernel for density, pdf, estimation pdfi = stats.gamma.pdf(sample, x / bw + 1, scale=bw) return pdfi
kernel_pdf_gamma.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_cdf_gamma(x, sample, bw): # Gamma kernel for density, pdf, estimation # kernel cdf uses the survival function, but I don't know why. cdfi = stats.gamma.sf(sample, x / bw + 1, scale=bw) return cdfi
kernel_cdf_gamma.__doc__ = """\ 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. """.format(doc_params=doc_params) def _kernel_pdf_gamma(x, sample, bw): """Gamma 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. """ return stats.gamma.pdf(sample, x / bw, scale=bw) def _kernel_cdf_gamma(x, sample, bw): """Gamma 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. """ return stats.gamma.sf(sample, x / bw, scale=bw)
[docs] def kernel_pdf_gamma2(x, sample, bw): # Gamma kernel for density, pdf, estimation with boundary correction if np.size(x) == 1: # without vectorizing, easier to read if x < 2 * bw: a = (x / bw)**2 + 1 else: a = x / bw else: a = x / bw mask = x < 2 * bw a[mask] = a[mask]**2 + 1 pdf = stats.gamma.pdf(sample, a, scale=bw) return pdf
kernel_pdf_gamma2.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_cdf_gamma2(x, sample, bw): # Gamma kernel for cdf estimation with boundary correction if np.size(x) == 1: # without vectorizing if x < 2 * bw: a = (x / bw)**2 + 1 else: a = x / bw else: a = x / bw mask = x < 2 * bw a[mask] = a[mask]**2 + 1 pdf = stats.gamma.sf(sample, a, scale=bw) return pdf
kernel_cdf_gamma2.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_pdf_invgamma(x, sample, bw): # Inverse gamma kernel for density, pdf, estimation return stats.invgamma.pdf(sample, 1 / bw + 1, scale=x / bw)
kernel_pdf_invgamma.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_cdf_invgamma(x, sample, bw): # Inverse gamma kernel for cumulative distribution, cdf, estimation return stats.invgamma.sf(sample, 1 / bw + 1, scale=x / bw)
kernel_cdf_invgamma.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_pdf_invgauss(x, sample, bw): # Inverse gaussian kernel for density, pdf, estimation m = x lam = 1 / bw return stats.invgauss.pdf(sample, m / lam, scale=lam)
kernel_pdf_invgauss.__doc__ = """\ 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. """.format(doc_params=doc_params) def kernel_pdf_invgauss_(x, sample, bw): """Inverse gaussian kernel density, explicit formula. Scaillet 2004 """ pdf = (1 / np.sqrt(2 * np.pi * bw * sample**3) * np.exp(- 1 / (2 * bw * x) * (sample / x - 2 + x / sample))) return pdf.mean(-1)
[docs] def kernel_cdf_invgauss(x, sample, bw): # Inverse gaussian kernel for cumulative distribution, cdf, estimation m = x lam = 1 / bw return stats.invgauss.sf(sample, m / lam, scale=lam)
kernel_cdf_invgauss.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_pdf_recipinvgauss(x, sample, bw): # Reciprocal inverse gaussian kernel for density, pdf, estimation # need shape-scale parameterization for scipy # references use m, lambda parameterization m = 1 / (x - bw) lam = 1 / bw return stats.recipinvgauss.pdf(sample, m / lam, scale=1 / lam)
kernel_pdf_recipinvgauss.__doc__ = """\ 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. """.format(doc_params=doc_params) def kernel_pdf_recipinvgauss_(x, sample, bw): """Reciprocal inverse gaussian kernel density, explicit formula. Scaillet 2004 """ pdf = (1 / np.sqrt(2 * np.pi * bw * sample) * np.exp(- (x - bw) / (2 * bw) * sample / (x - bw) - 2 + (x - bw) / sample)) return pdf
[docs] def kernel_cdf_recipinvgauss(x, sample, bw): # Reciprocal inverse gaussian kernel for cdf estimation # need shape-scale parameterization for scipy # references use m, lambda parameterization m = 1 / (x - bw) lam = 1 / bw return stats.recipinvgauss.sf(sample, m / lam, scale=1 / lam)
kernel_cdf_recipinvgauss.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_pdf_bs(x, sample, bw): # Birnbaum Saunders (normal) kernel for density, pdf, estimation return stats.fatiguelife.pdf(sample, bw, scale=x)
kernel_pdf_bs.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_cdf_bs(x, sample, bw): # Birnbaum Saunders (normal) kernel for cdf estimation return stats.fatiguelife.sf(sample, bw, scale=x)
kernel_cdf_bs.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_pdf_lognorm(x, sample, bw): # Log-normal kernel for density, pdf, estimation # need shape-scale parameterization for scipy # not sure why JK picked this normalization, makes required bw small # maybe we should skip this transformation and just use bw # Funke and Kawka 2015 (table 1) use bw (or bw**2) corresponding to # variance of normal pdf # bw = np.exp(bw_**2 / 4) - 1 # this is inverse transformation bw_ = np.sqrt(4*np.log(1+bw)) return stats.lognorm.pdf(sample, bw_, scale=x)
kernel_pdf_lognorm.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_cdf_lognorm(x, sample, bw): # Log-normal kernel for cumulative distribution, cdf, estimation # need shape-scale parameterization for scipy # not sure why JK picked this normalization, makes required bw small # maybe we should skip this transformation and just use bw # Funke and Kawka 2015 (table 1) use bw (or bw**2) corresponding to # variance of normal pdf # bw = np.exp(bw_**2 / 4) - 1 # this is inverse transformation bw_ = np.sqrt(4*np.log(1+bw)) return stats.lognorm.sf(sample, bw_, scale=x)
kernel_cdf_lognorm.__doc__ = """\ 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. """.format(doc_params=doc_params) def kernel_pdf_lognorm_(x, sample, bw): """Log-normal kernel for density, pdf, estimation, explicit formula. Jin, Kawczak 2003 """ term = 8 * np.log(1 + bw) # this is 2 * variance in normal pdf pdf = (1 / np.sqrt(term * np.pi) / sample * np.exp(- (np.log(x) - np.log(sample))**2 / term)) return pdf.mean(-1)
[docs] def kernel_pdf_weibull(x, sample, bw): # Weibull kernel for density, pdf, estimation # need shape-scale parameterization for scipy # references use m, lambda parameterization return stats.weibull_min.pdf(sample, 1 / bw, scale=x / special.gamma(1 + bw))
kernel_pdf_weibull.__doc__ = """\ 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. """.format(doc_params=doc_params)
[docs] def kernel_cdf_weibull(x, sample, bw): # Weibull kernel for cumulative distribution, cdf, estimation # need shape-scale parameterization for scipy # references use m, lambda parameterization return stats.weibull_min.sf(sample, 1 / bw, scale=x / special.gamma(1 + bw))
kernel_cdf_weibull.__doc__ = """\ 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. """.format(doc_params=doc_params) # produced wth # print("\n".join(['"%s": %s,' % (i.split("_")[-1], i) for i in dir(kern) # if "kernel" in i and not i.endswith("_")])) kernel_dict_cdf = { "beta": kernel_cdf_beta, "beta2": kernel_cdf_beta2, "bs": kernel_cdf_bs, "gamma": kernel_cdf_gamma, "gamma2": kernel_cdf_gamma2, "invgamma": kernel_cdf_invgamma, "invgauss": kernel_cdf_invgauss, "lognorm": kernel_cdf_lognorm, "recipinvgauss": kernel_cdf_recipinvgauss, "weibull": kernel_cdf_weibull, } kernel_dict_pdf = { "beta": kernel_pdf_beta, "beta2": kernel_pdf_beta2, "bs": kernel_pdf_bs, "gamma": kernel_pdf_gamma, "gamma2": kernel_pdf_gamma2, "invgamma": kernel_pdf_invgamma, "invgauss": kernel_pdf_invgauss, "lognorm": kernel_pdf_lognorm, "recipinvgauss": kernel_pdf_recipinvgauss, "weibull": kernel_pdf_weibull, }

Last update: Apr 12, 2024