On infinitely divisible multivariate gamma distributions

Stephen G. Walker

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 13, 4484-4490

Abstract: We provide an explicit construction of variables from a bivariate gamma distribution which is infinitely divisible. These distributions are currently only known through their (complicated) density functions or moment generating functions. The sampling construction uses independent gamma and Poisson random variables and sheds further light on these distributions and their infinitely divisible property. The extension to multivariate gamma infinitely divisible variables is also provided, as well as a negative binomial case.

Date: 2023
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DOI: 10.1080/03610926.2021.1995431

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