Characterization of count data distributions involving additivity and binomial subsampling

Pedro Puig, Jordi Valero

Research output: Contribution to journalArticleResearchpeer-review

16 Citations (Scopus)

Abstract

In this paper we characterize all the r-parameter families of count distributions (satisfying mild conditions) that are closed under addition and under binomial subsampling. Surprisingly, few families satisfy both properties and the resulting models consist of the rth-order univariate Hermite distributions. Among these, we find the Poisson (r = 1) and the ordinary Hermite distributions (r = 2). © 2007 ISI/BS.
Original languageEnglish
Pages (from-to)544-555
JournalBernoulli
Volume13
DOIs
Publication statusPublished - 1 Dec 2007

Keywords

  • Closed under addition
  • Hermite distribution
  • Independent p-thinning
  • Mixed Poisson distribution
  • Overdispersion
  • Top inverse

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