Some characterizations and properties of COM-Poisson random variables

Bo Li, Huiming Zhang and Jiao He

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 6, 1311-1329

Abstract: Starting with a literature review for theoretical properties of COM-Poisson distributions, this paper proposes some new characterizations of COM-Poisson random variables. First, we extend the Moran-Chatterji characterization and generalize the Rao-Rubin characterization of Poisson distribution to COM-Poisson distribution. Then, we define the COM-type discrete r.v. Xν of the discrete random variable X. The probability mass function of Xν 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 is obtained. Finally, under the property of “not closed under addition” of COM-Poisson random variables, a new characterization of Poisson distribution is found.

Date: 2020
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DOI: 10.1080/03610926.2018.1563164

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