statsmodels.distributions.copula.api.ClaytonCopula

class statsmodels.distributions.copula.api.ClaytonCopula(theta=None, k_dim=2)

Clayton copula.

Dependence is greater in the negative tail than in the positive.

\[C_\theta(u,v) = \left[ \max\left\{ u^{-\theta} + v^{-\theta} -1 ; 0 \right\} \right]^{-1/\theta}\]

with \(\theta\in[-1,\infty)\backslash\{0\}\).

Parameters:

thetafloat, optional

Parameter of the copula, must be > -1 and != 0. If not provided, then the copula parameter must be provided as args when calling methods.

k_dimint, optional

Dimension, number of components in the multivariate random variable.

Methods

cdf(u[, args])	Evaluate cdf of the Clayton copula.
fit_corr_param(data)	Copula correlation parameter using Kendall's tau of sample data.
logpdf(u[, args])	Evaluate log-pdf of the Clayton copula.
pdf(u[, args])	Evaluate pdf of the Clayton copula.
plot_pdf([ticks_nbr, ax])	Plot the PDF.
plot_scatter([sample, nobs, rng, ax])	Sample the copula and plot.
rvs([nobs, args, rng])	Generate random variates from the copula.
tau([theta])	Kendall's tau as a function of the copula parameter theta.
tau_simulated([nobs, rng])	Kendall's tau based on simulated samples.
theta_from_tau(tau)	Compute the copula parameter theta from Kendall's tau.

Methods

cdf(u[, args])	Evaluate cdf of the Clayton copula.
fit_corr_param(data)	Copula correlation parameter using Kendall's tau of sample data.
logpdf(u[, args])	Evaluate log-pdf of the Clayton copula.
pdf(u[, args])	Evaluate pdf of the Clayton copula.
plot_pdf([ticks_nbr, ax])	Plot the PDF.
plot_scatter([sample, nobs, rng, ax])	Sample the copula and plot.
rvs([nobs, args, rng])	Generate random variates from the copula.
tau([theta])	Kendall's tau as a function of the copula parameter theta.
tau_simulated([nobs, rng])	Kendall's tau based on simulated samples.
theta_from_tau(tau)	Compute the copula parameter theta from Kendall's tau.