Abstract: In this article we propose multivariate versions of the beta mixture of Poisson distribution considered by Gurland (1958), Katti (1966), and Holla and Bhattacharya (1965). The new class of distributions can be used for modeling multivariate dependent count data when marginal overdispersion is observed. After revising briefly some of their properties, a general multivariate model with Poisson-Beta marginals and with a flexible covariance structure is proposed. Several specific models as well as a model which admits correlations of any sign are considered. Estimation methods are discussed. Finally, examples of application for bivariate frequencies data are given.

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