Source code for statsmodels.distributions.copula.other_copulas

# -*- coding: utf-8 -*-
Created on Fri Jan 29 19:19:45 2021

Author: Josef Perktold
License: BSD-3

import numpy as np
from scipy import stats

from import check_random_state
from statsmodels.distributions.copula.copulas import Copula

[docs]class IndependenceCopula(Copula): """Independence copula. Copula with independent random variables. .. math:: C_\theta(u,v) = uv Parameters ---------- k_dim : int Dimension, number of components in the multivariate random variable. Notes ----- IndependenceCopula does not have copula parameters. If non-empty ``args`` are provided in methods, then a ValueError is raised. The ``args`` keyword is provided for a consistent interface across copulas. """ def __init__(self, k_dim=2): super().__init__(k_dim=k_dim) def _handle_args(self, args): if args != () and args is not None: msg = ("Independence copula does not use copula parameters.") raise ValueError(msg) else: return args
[docs] def rvs(self, nobs=1, args=(), random_state=None): self._handle_args(args) rng = check_random_state(random_state) x = rng.random((nobs, self.k_dim)) return x
[docs] def pdf(self, u, args=()): return np.ones(len(u))
[docs] def cdf(self, u, args=()): return, axis=1)
[docs] def tau(self): return 0
[docs] def plot_pdf(self, *args): raise NotImplementedError("PDF is constant over the domain.")
def rvs_kernel(sample, size, bw=1, k_func=None, return_extras=False): """Random sampling from empirical copula using Beta distribution Parameters ---------- sample : ndarray Sample of multivariate observations in (o, 1) interval. size : int Number of observations to simulate. bw : float Bandwidth for Beta sampling. The beta copula corresponds to a kernel estimate of the distribution. bw=1 corresponds to the empirical beta copula. A small bandwidth like bw=0.001 corresponds to small noise added to the empirical distribution. Larger bw, e.g. bw=10 corresponds to kernel estimate with more smoothing. k_func : None or callable The default kernel function is currently a beta function with 1 added to the first beta parameter. return_extras : bool If this is False, then only the random sample will be returned. If true, then extra information is returned that is mainly of interest for verification. Returns ------- rvs : ndarray Multivariate sample with ``size`` observations drawn from the Beta Copula. Notes ----- Status: experimental, API will change. """ # vectorized for observations n = sample.shape[0] if k_func is None: kfunc = _kernel_rvs_beta1 idx = np.random.randint(0, n, size=size) xi = sample[idx] krvs = np.column_stack([kfunc(xii, bw) for xii in xi.T]) if return_extras: return krvs, idx, xi else: return krvs def _kernel_rvs_beta(x, bw): # Beta kernel for density, pdf, estimation return stats.beta.rvs(x / bw + 1, (1 - x) / bw + 1, size=x.shape) def _kernel_rvs_beta1(x, bw): # Beta kernel for density, pdf, estimation # Kiriliouk, Segers, Tsukuhara 2020 arxiv, using bandwith 1/nobs sample return stats.beta.rvs(x / bw, (1 - x) / bw + 1)