Source code for statsmodels.distributions.copula.extreme_value

# -*- coding: utf-8 -*-
""" Extreme Value Copulas
Created on Fri Jan 29 19:19:45 2021

Author: Josef Perktold
License: BSD-3

"""

import numpy as np
from .copulas import Copula


def copula_bv_ev(u, transform, args=()):
    '''generic bivariate extreme value copula
    '''
    u, v = u
    return np.exp(np.log(u * v) * (transform(np.log(u)/np.log(u*v), *args)))


[docs]class ExtremeValueCopula(Copula): """Extreme value copula constructed from Pickand's dependence function. Currently only bivariate copulas are available. Parameters ---------- transform: instance of transformation class Pickand's dependence function with required methods including first and second derivatives args : tuple Optional copula parameters. Copula parameters can be either provided when creating the instance or as arguments when calling methods. k_dim : int Currently only bivariate extreme value copulas are supported. Notes ----- currently the following dependence function and copulas are available - AsymLogistic - AsymNegLogistic - AsymMixed - HR TEV and AsymBiLogistic currently do not have required derivatives for pdf. See Also -------- dep_func_ev """ def __init__(self, transform, args=(), k_dim=2): super().__init__(k_dim=k_dim) self.transform = transform self.k_args = transform.k_args self.args = args def _handle_args(self, args): # TODO: how to we handle non-tuple args? two we allow single values? # Model fit might give an args that can be empty if isinstance(args, np.ndarray): args = tuple(args) # handles empty arrays, unpacks otherwise if args == () or args is None: args = self.args if not isinstance(args, tuple): args = (args,) return args
[docs] def cdf(self, u, args=()): """Evaluate cdf of bivariate extreme value copula. Parameters ---------- u : array_like Values of random bivariate random variable, each defined on [0, 1], for which cdf is computed. Can be two dimensional with multivariate components in columns and observation in rows. args : tuple Required parameters for the copula. The meaning and number of parameters in the tuple depends on the specific copula. Returns ------- CDF values at evaluation points. """ # currently only Bivariate u, v = np.asarray(u).T args = self._handle_args(args) cdfv = np.exp(np.log(u * v) * self.transform(np.log(u)/np.log(u*v), *args)) return cdfv
[docs] def pdf(self, u, args=()): """Evaluate pdf of bivariate extreme value copula. Parameters ---------- u : array_like Values of random bivariate random variable, each defined on [0, 1], for which cdf is computed. Can be two dimensional with multivariate components in columns and observation in rows. args : tuple Required parameters for the copula. The meaning and number of parameters in the tuple depends on the specific copula. Returns ------- PDF values at evaluation points. """ tr = self.transform u1, u2 = np.asarray(u).T args = self._handle_args(args) log_u12 = np.log(u1 * u2) t = np.log(u1) / log_u12 cdf = self.cdf(u, args) dep = tr(t, *args) d1 = tr.deriv(t, *args) d2 = tr.deriv2(t, *args) pdf_ = cdf / (u1 * u2) * ((dep + (1 - t) * d1) * (dep - t * d1) - d2 * (1 - t) * t / log_u12) return pdf_
[docs] def logpdf(self, u, args=()): """Evaluate log-pdf of bivariate extreme value copula. Parameters ---------- u : array_like Values of random bivariate random variable, each defined on [0, 1], for which cdf is computed. Can be two dimensional with multivariate components in columns and observation in rows. args : tuple Required parameters for the copula. The meaning and number of parameters in the tuple depends on the specific copula. Returns ------- Log-pdf values at evaluation points. """ return np.log(self.pdf(u, args=args))
[docs] def conditional_2g1(self, u, args=()): """conditional distribution not yet implemented C2|1(u2|u1) := ∂C(u1, u2) / ∂u1 = C(u1, u2) / u1 * (A(t) − t A'(t)) where t = np.log(v)/np.log(u*v) """ raise NotImplementedError