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Abstract
In this article we propose multivariate versions of the beta mixture of Poisson distribution considered by Gurland (Citation1958), Katti (Citation1966), and Holla and Bhattacharya (Citation1965). 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.
Acknowledgments
The authors thanks Ministerio de Ciencia e Innovación (projects SEJ2007-65818 (JMS) and SEJ2006-12685 (EGD)) for partial support of this work. The first author also thanks to Ministerio de Educación of Spain (PR2009-0200, Programa Nacional de Movilidad de Recursos Humanos) for support. We are grateful for the constructive suggestions provided by Associate Editor and the referees, which have improved the article.
