Marshall–Olkin Laplace transform copulas of multivariate gamma distributions

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, …, θ_n.

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

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E15
• 60E10
• 60E07
• 62H20

Acknowledgments

I thank Gérard Letac for many helpful conversations.