
























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.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。