some new features

.venv/lib/python3.12/site-packages/statsmodels/nonparametric/kernels_asymmetric.py

@@ -0,0 +1,824 @@
+"""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"""
+
+
+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
+
+
+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
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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)
+
+
+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,
+    }