statsmodels.distributions.copula.api.FrankCopula

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

Frank copula.

Dependence is symmetric.

\[C_\theta(\mathbf{u}) = -\frac{1}{\theta} \log \left[ 1- \frac{ \prod_j (1-\exp(- \theta u_j)) }{ (1 - \exp(-\theta)-1)^{d - 1} } \right]\]

with \(\theta\in \mathbb{R}\backslash\{0\}, \mathbf{u} \in [0, 1]^d\).

Parameters:

thetafloat, optional

Parameter of the copula, must be != 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 Frank copula.
cdfcond_2g1(u[, args])	Conditional cdf of second component given the value of first.
fit_corr_param(data)	Copula correlation parameter using Kendall's tau of sample data.
logpdf(u[, args])	Evaluate log-pdf of the Frank copula.
pdf(u[, args])	Evaluate pdf of the Frank copula.
plot_pdf([ticks_nbr, ax])	Plot the PDF.
plot_scatter([sample, nobs, rng, ax])	Sample the copula and plot.
ppfcond_2g1(q, u1[, args])	Conditional ppf (quantile) of second component given first.
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 Frank copula.
cdfcond_2g1(u[, args])	Conditional cdf of second component given the value of first.
fit_corr_param(data)	Copula correlation parameter using Kendall's tau of sample data.
logpdf(u[, args])	Evaluate log-pdf of the Frank copula.
pdf(u[, args])	Evaluate pdf of the Frank copula.
plot_pdf([ticks_nbr, ax])	Plot the PDF.
plot_scatter([sample, nobs, rng, ax])	Sample the copula and plot.
ppfcond_2g1(q, u1[, args])	Conditional ppf (quantile) of second component given first.
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.