The Conway-Maxwell-Poisson distribution: Distributional theory and approximation

Fraser A Daly, Robert Gaunt

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Abstract

The Conway-Maxwell-Poisson (CMP) distribution is a natural two-parameter generalisation of the Poisson distribution which has received some attention in the statistics literature in recent years by offering flexible generalisations of some well-known models. In this work, we begin by establishing some properties of both the CMP distribution and an analogous generalisation of the binomial distribution, which we refer to as the CMB distribution. We also consider some convergence results and approximations, including a bound on the total variation distance between a CMB distribution and the corresponding CMP limit.
Original languageEnglish
Pages (from-to)635–658
Number of pages24
JournalALEA: Latin American Journal of Probability and Mathematical Statistics
Volume13
Issue number2
Early online date31 Jul 2016
Publication statusPublished - 2016

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