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arXiv · 1809.09567

Some Characterizations and Properties of COM-Poisson Random Variables

Bo Li·Huiming Zhang·Jiao He
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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 ($ν\ne 1$) 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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Bo Li, Huiming Zhang, Jiao He. 2018-09-25. Some Characterizations and Properties of COM-Poisson Random Variables. https://arxiv.org/abs/1809.09567

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