Copula families, properties and methods

Families

The copul package covers implementations of the following copula families:

• Archimedean copula families including Clayton, Gumbel, Frank, Joe, Ali-Mikhail-Haq, and more

• Extreme-value copulas families like Hüsler-Reiss, Galambos, Marshall-Olkin, etc.

• Elliptical copula families: Gaussian, Student’s t, and Laplace.

• Unclassified copula families like the Plackett or Raftery copula families.

Furthermore, the package provides the following copulas:

• Independence copula

• Lower and upper Fréchet bounds

• Checkerboard copulas

A list of all implemented copulas can be found in copul.Families.

Properties

The following properties are available for the above copula families and copulas if they exist and are known:

• cdf: Cumulative distribution function

• pdf: Probability density function

• cond_distr_1, cond_distr_2: Conditional distribution functions

• lambda_L, lambda_U: Lower and upper tail dependence coefficients

• rho, tau, xi: Spearman’s rho, Kendall’s tau, and Chatterjee’s xi

• generator, inv_generator: Generator and inverse generator for Archimedean copula families

• pickands: Pickands dependence functions for extreme-value copula families

Methods

The following methods are available for the above copula families and copulas:

• rvs: Generate random samples from the copula

• scatter_plot: Generate a scatter plot of the copula

• plot_cdf: Visualize the cumulative distribution function

• plot_pdf: Visualize the probability density function

• plot_rank_correlations: Visualize Spearman’s rho, Kendall’s tau, and Chatterjee’s xi

• plot_generator: Visualize the generator function

• plot_pickands: Visualize the Pickands dependence function