Characterizing additively closed discrete models by a property of their maximum likelihood estimators, with an application to generalized hermite distributions

• 成果类型: Article
• 署名作者: Puig, P
• 署名单位: Autonomous University of Barcelona
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214503000000594
• 发表日期: 2003
• 页码: 687-692
• 关键词: parameters

摘要

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.