Mixture of the Riesz distribution with respect to the multivariate Poisson

TL;DR

This paper investigates a new mixture model combining the Riesz distribution on symmetric matrices with the multivariate Poisson distribution, exploring its mathematical properties and related exponential family.

Contribution

It introduces a novel mixture distribution, analyzes its connection to the modified Bessel function, and characterizes its natural exponential family including mean domain and variance.

Findings

Distribution related to modified Bessel function

Determined mean domain of the exponential family

Analyzed variance function of the family

Abstract

The aim of this paper is to study the mixture of the Riesz distribution on symmetric matrices with respect to the multivariate Poisson distribution. We show, in particular, that this distribution is related to the modified Bessel function of the first kind. We also study the generated natural exponential family. We determine the domain of the means and the variance function of this family.