copul is a package designed for mathematical computation with and visualization of bivariate copula families.

Install the copul library using pip.

pip install copul

A guide and documentation is available at https://copul.readthedocs.io/.

The copul package covers implementations of the following copula families:

• Archimedean copula families: The 22 Archimedean copula families from the book "Nelsen - An Introduction to Copulas" including
  • Clayton
  • Gumbel-Hougaard
  • Frank
  • Joe
  • Ali-Mikhail-Haq
  • etc.
• Extreme-value copulas families:
  • BB5
  • Cuadras-Augé
  • Galambos
  • Gumbel
  • Husler-Reiss
  • Joe
  • Marshall-Olkin
  • tEV
  • Tawn
• Elliptical copula families:
  • Gaussian
  • Student's t
  • Laplace.
• Other copula families:
  • Farlie-Gumbel-Morgenstern
  • Fréchet
  • Mardia
  • Plackett
  • Raftery

Furthermore, the package provides the following copulas:

• Independence copula
• Lower and upper Fréchet bounds
• Checkerboard copulas

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

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