Marshall–Olkin Laplace transform copulas of multivariate gamma distributions

Philippe Bernardoff

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 3, 655-670

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 [P(θ)]-λ$[P(\boldsymbol{\theta })]^{-\lambda }$ and [P(θ)]-λ∏i=1n(1+piθi)-(λi-λ)$[P(\boldsymbol{\theta })]^{-\lambda }\prod _{i=1}^{n}(1+p_{i}\theta _{i})^{-(\lambda _{i}-\lambda)}$, 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.

Date: 2018
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DOI: 10.1080/03610926.2017.1310241

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