ABSTRACT
This article provides two copula families on [0, 1]n obtained from the Laplace transforms of the multivariate gamma distribution and the multifactor gamma distribution given by and
, respectively, where P is an affine polynomial with respect to the n variables θ1, …, θn.
These copulas allow in particular to obtain multivariate gamma distributions for which the cumulative distribution functions and the probability distribution functions are known.
KEYWORDS:
- Copula
- Cumulative distribution function
- Exponential families
- Generalized hypergeometric function
- Generalized Lauricella functions
- Horn function
- Infinitely divisible distribution
- Kendall's tau
- Laplace transform
- Marshall–Olkin Laplace transform copula
- Multifactor gamma distribution
- Multivariate gamma distribution
- Spearman's rho
Acknowledgments
I thank Gérard Letac for many helpful conversations.