Mixture of the Riesz distribution with respect to the multivariate Poisson

Abdelhamid Hassairi (1) , Mahdi Louati (1)

1 Laboratory of Probability and Statistics

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.

Mots clés: Mixed distribution; Riesz distribution; Bessel function; natural exponential family; variance function

Domaines: Probabilités [math.PR]

Abdelhamid Hassairi, Mahdi Louati. Mixture of the Riesz distribution with respect to the multivariate Poisson. 2009. ⟨hal-00351710⟩