Source code for statsmodels.distributions.copula.extreme_value
""" 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
if k_dim != 2:
raise ValueError("Only bivariate EV copulas are available.")
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
Last update:
Apr 19, 2024