copul 0.0.12

Mathematical computation and visualization of bivariate copulas.

copul

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

Install

Install the copul library using pip.

pip install copul

Documentation

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

Copula properties

For any of the bivariate copula families specified below, e.g. copula = copul.Galambos(), get the following properties (if applicable):

• Cumulative distribution function via copula.cdf
• Density function via copula.pdf
• Conditional distribution function via copula.cond_distr_1 and copula.cond_distr_2
• Data sampling from the copula via copula.rvs. The number of samples can be specified as an argument, e.g. copula.rvs(1000)

The following measures of association and dependence are also added if closed-forms are known:

• copula.lambda_L - lower tail dependence coefficient
• copula.lambda_U - upper tail dependence coefficient
• copula.tau - Kendall's tau
• copula.rho - Spearman's rho
• copula.xi - Chatterjee's xi

Supported copula families:

Archimedean Copulas

The 22 Archimedean copula families from the book "Nelsen - An Introduction to Copulas", accessible via copul.archimedean.Nelsen1, copul.archimedean.Nelsen2, etc. Let copula be any instance of those classes, e.g. copula = copul.archimedean.Nelsen1().

For these families, the following properties are available:

• generator function is available via e.g. copula.generator
• inverse generator function is available via e.g. copula.inverse_generator
• CI char function is available via e.g. copula.ci_char
• the MTP2 char function is available via e.g. copula.mtp2_char

Extreme Value Copulas

• BB5
• Cuadras-Augé
• Galambos
• Gumbel
• Husler-Reiss
• Joe
• Marshall-Olkin
• tEV
• tawn

Let copula be any instance of those classes, e.g. copula = copul.extreme_value.Galambos(). Then, the Pickands function is available via e.g. copula.pickands.

Elliptical Copulas

• Gaussian
• Student-t
• Laplace

Other

• Farlie-Gumbel-Morgenstern
• Fréchet
• Mardia
• Plackett
• Raftery