Count data distributions: Some characterizations with applications

Pedro Puig, Jordi Valero

Research output: Contribution to journalArticleResearchpeer-review

66 Citations (Scopus)


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. © 2006 American Statistical Association.
Original languageEnglish
Pages (from-to)332-340
JournalJournal of the American Statistical Association
Publication statusPublished - 1 Mar 2006


  • Closed under addition
  • Exploratory data analysis
  • Exponential dispersion model
  • Mixed Poisson
  • Overdispersion
  • Stopped Poisson
  • Zero inflation


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