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

Gaussian copula.

It is constructed from a multivariate normal distribution over \(\mathbb{R}^d\) by using the probability integral transform.

For a given correlation matrix \(R \in[-1, 1]^{d \times d}\), the Gaussian copula with parameter matrix \(R\) can be written as:

\[C_R^{\text{Gauss}}(u) = \Phi_R\left(\Phi^{-1}(u_1),\dots, \Phi^{-1}(u_d) \right),\]

where \(\Phi^{-1}\) is the inverse cumulative distribution function of a standard normal and \(\Phi_R\) is the joint cumulative distribution function of a multivariate normal distribution with mean vector zero and covariance matrix equal to the correlation matrix \(R\).

corrscalar or array_like

Correlation or scatter matrix for the elliptical copula. In the bivariate case, corr` can be a scalar and is then considered as the correlation coefficient. If ``corr is None, then the scatter matrix is the identity matrix.


Dimension, number of components in the multivariate random variable.


Elliptical copulas require that copula parameters are set when the instance is created. Those parameters currently cannot be provided in the call to methods. (This will most likely change in future versions.) If non-empty args are provided in methods, then a ValueError is raised. The args keyword is provided for a consistent interface across copulas.



Joe, Harry, 2014, Dependence modeling with copulas. CRC press. p. 163


cdf(u[, args])

Cumulative distribution function evaluated at points u.


Pearson correlation from kendall’s tau.


Bivariate tail dependence parameter.


Copula correlation parameter using Kendall’s tau of sample data.

logpdf(u[, args])

Log of copula pdf, loglikelihood.

pdf(u[, args])

Probability density function of copula.

plot_pdf([ticks_nbr, ax])

Plot the PDF.

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

Sample the copula and plot.

rvs([nobs, args, random_state])

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


Bivariate kendall’s tau based on correlation coefficient.

tau_simulated([nobs, random_state])

Kendall’s tau based on simulated samples.