A bivariate mixture of negative binomial distributions and its applications

Abstract

We construct a new bivariate mixture of negative binomial distributions which represents over-dispersed data more efficiently. This is an extension of a univariate mixture of beta and negative binomial distributions. Characteristics of this joint distribution are studied including conditional distributions. Some properties of the correlation coefficient are explored. We demonstrate the applicability of our proposed model by fitting to three real data sets with correlated count data. A comparison is made with some previously used models to show the effectiveness of the new model.

Keywords:

• Bivariate beta distribution
• generalized hypergeometric function
• multivariate discrete distribution
• numerical estimation
• over-dispersion

Acknowledgments

The authors are thankful to the two reviewers for their valuable suggestions which have substantially improved the content and the presentation of the paper. We also thank Professor Bo Martin Bibby for some helpful suggestions.