Count Data Distributions
- 1 March 2006
- journal article
- Published by Taylor & Francis in Journal of the American Statistical Association
- Vol. 101 (473) , 332-340
- https://doi.org/10.1198/016214505000000718
Abstract
In this article we characterize all two-parameter count distributions (satisfying very general conditions) that are partially closed under addition. We also find those for which the maximum likelihood estimator of the population mean is the sample mean. Mixed Poisson models satisfying these properties are completely determined. Among these models are the negative binomial, Poisson-inverse Gaussian, and other known distributions. New count distributions can also be constructed using these characterizations. Three examples of application are given.Keywords
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