Overdispersed and underdispersed Poisson generalizations

Joan del Castillo, Marta Pérez-Casany

Research output: Contribution to journalArticleResearchpeer-review

57 Citations (Scopus)


We consider a wide set of statistical models that extend the Poisson distribution. These models are obtained through weighted versions of the Poisson family and can be approximated by a log-linear model. Under general conditions, we prove that the new models contain overdispersed and underdispersed distributions and that they can be parametrized with the mean and variance. A classical data set is analyzed to show the usefulness of the new models. © 2004 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)486-500
JournalJournal of Statistical Planning and Inference
Publication statusPublished - 1 Oct 2005


  • Exponential models
  • Index of dispersion
  • Stochastic orders
  • Weighted distributions
  • Zero-inflated distributions


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