statsmodels.distributions.copula.api.FrankCopula

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

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

Methods

cdf(u[, args])

Evaluate cdf of Archimedean 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 multivariate Archimedean copula.

pdf(u[, args])

Evaluate pdf of Archimedean copula.

plot_pdf([ticks_nbr, ax])

Plot the PDF.

plot_scatter([sample, nobs, random_state, ax])

Sample the copula and plot.

ppfcond_2g1(q, u1[, args])

Conditional pdf of second component given the value of first.

rvs([nobs, args, random_state])

Draw n in the half-open interval [0, 1).

tau([theta])

tau_simulated([nobs, random_state])

Kendall’s tau based on simulated samples.

theta_from_tau(tau)