Laplace copulas of multifactor gamma distributions are new generalized Farlie-Gumbel-Morgenstern copulas

TL;DR

This paper introduces new copula families derived from Laplace transforms of multivariate gamma distributions, enabling the construction of multivariate gamma distributions with known distribution functions.

Contribution

It presents novel generalized Farlie-Gumbel-Morgenstern copulas based on Laplace transforms of multi-factor gamma distributions, expanding the tools for modeling multivariate gamma distributions.

Findings

New bifactor and trivariate gamma distributions introduced.

Derived copulas allow explicit distribution and density functions.

Provides a framework for multivariate gamma modeling.

Abstract

This paper provides bifactor gamma distribution, trivariate gamma distribution and two copula families on [0, 1] n obtained from the Laplace transforms of the multivariate gamma distribution and the multi-factor gamma distribution given by [P ($\theta$)] --$\lambda$ and [P ($\theta$)] --$\lambda$ n i=1 (1 + pi$\theta$i) --($\lambda$ i --$\lambda$) respectively, where P is an affine polynomial with respect to the n variables $\theta$1,. .. , $\theta$n. These copulas are new generalized Farlie-Gumbel-Morgenstern copulas and allow in particular to obtain multivariate gamma distributions for which the cumulative distribution functions and the probability distribution functions are known.