Characterizing Additively Closed Discrete Models by a Property of their Maximum Likelihood Estimators, with an Application to Generalized Hermite Distributions

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Abstract

This article reports on two-parameter count distributions (satisfying very general conditions) that are closed under addition so that their maximum likelihood estimator (MLE) of the population mean is the sample mean. The most important of these in practice, the generalized Hermite distribution, is analyzed, and a necessary and sufficient condition is given to ensure that the MLE is the solution of likelihood equations. Score test to contrast the Poisson assumption is studied, and two examples of applications are given.
Original languageEnglish
Pages (from-to)687-692
JournalJournal of the American Statistical Association
Volume98
DOIs
Publication statusPublished - 1 Sep 2003

Keywords

  • Count data
  • Hermite distribution
  • Nonregular models
  • Overdispersion
  • Poisson-normal distribution
  • Zero inflation

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