Multivariate Poisson-Beta Distributions with Applications

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...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2011-01, Vol.40 (6), p.1093-1108
Main Authors: Sarabia, José María, Gómez-Déniz, Emilio
Format: Article
Language:English
Subjects:
Beta
Correlation
Counting
Covariance
Distribution theory
Exact sciences and technology
General topics
Mathematical models
Mathematics
Multivariate analysis
Overdispersion
Poisson distributions
Poisson-Beta distribution
Probability and statistics
Probability theory and stochastic processes
Sarmanov-Lee family
Sciences and techniques of general use
Statistics
Studies
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Summary: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.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610920903537269