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Some characterizations and properties of COM-Poisson random variables

Author

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  • Bo Li
  • Huiming Zhang
  • Jiao He

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.

Suggested Citation

  • Bo Li & Huiming Zhang & Jiao He, 2020. "Some characterizations and properties of COM-Poisson random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(6), pages 1311-1329, March.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:6:p:1311-1329
    DOI: 10.1080/03610926.2018.1563164
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    Cited by:

    1. Geng, Xi & Xia, Aihua, 2022. "When is the Conway–Maxwell–Poisson distribution infinitely divisible?," Statistics & Probability Letters, Elsevier, vol. 181(C).

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