Some Characterizations and Properties of COM-Poisson Random Variables

2018/09/25 by Bo Li, Li, Bo, Huiming Zhang +3
Decision Sciences · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1809.09567

openalex publication_date 2018/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces some new characterizations of COM-Poisson random variables. First, it extends Moran-Chatterji characterization and generalizes Rao-Rubin characterization of Poisson distribution to COM-Poisson distribution. Then, it defines the COM-type discrete r.v. X_ν of the discrete random variable X. The probability mass function of X_ν has a link to the Rényi entropy and Tsallis entropy of order ν of X. And then we can get the characterization of Stam inequality for COM-type discrete version Fisher information. By using the recurrence formula, the property that COM-Poisson random variables (ν≠ 1) is not closed under addition are obtained. Finally, under the property of "not closed under addition" of COM-Poisson random variables, a new characterization of Poisson distribution is found.

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