Mathematical computation and visualization of bivariate copulas.
Project description
copul
copul is a package designed for mathematical computation with 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 families and copulas
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
Copula properties
The following properties are available for the above copula families and copulas if they exist and are known:
cdf
: Cumulative distribution functionpdf
: Probability density functioncond_distr_1
,cond_distr_2
: Conditional distribution functionslambda_L
,lambda_U
: Lower and upper tail dependence coefficientsrho
,tau
,xi
: Spearman's rho, Kendall's tau, and Chatterjee's xigenerator
,inv_generator
: Generator and inverse generator for Archimedean copula familiespickands
: Pickands dependence functions for extreme-value copula families
Copula methods
The following methods are available for the above copula families and copulas:
rvs
: Generate random samples from the copulascatter_plot
: Generate a scatter plot of the copulaplot_cdf
: Visualize the cumulative distribution functionplot_pdf
: Visualize the probability density functionplot_rank_correlations
: Visualize Spearman's rho, Kendall's tau, and Chatterjee's xiplot_generator
: Visualize the generator functionplot_pickands
: Visualize the Pickands dependence function
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