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

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 ($θ$)] --$λ$ and [P ($θ$)] --$λ$ n i=1 (1 + pi$θ$i) --($λ$ i --$λ$) respectively, where P is an affine polynomial with respect to the n variables $θ$1,. .. , $θ$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.