copul 0.0.3

Risk analysis with copulas.

copulas_in_systemic_risk

Copula properties

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

• Cumulative distribution function via copula.cdf
• Density function via copula.pdf

Supported copula families:

Archimedean Copulas

The 22 copula families from Nelsen, 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
• 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 Pickand function is available via e.g. copula.pickand.

Other

• Farlie-Gumbell-Morgenstern
• Frechet
• Plackett

Sample Usage

import copul

galambos = copul.extreme_value.Galambos()
params = galambos.sample_parameters(3)
galambos.plot_pickand(params)

clayton = copul.archimedean.Clayton()
clayton(theta=1.5).plot_cdf()
clayton(theta=2.5).plot_pdf()