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Characterizations of discrete compound Poisson distributions

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  • Huiming Zhang
  • Bo Li

Abstract

The aim of this paper is to give some new characterizations of discrete compound Poisson distributions. Firstly, we give a characterization by the Lévy–Khintchine formula of infinitely divisible distributions under some conditions. The second characterization need to present by row sum of random triangular arrays converges in distribution. And we give an application in probabilistic number theory, the strongly additive function converging to a discrete compound Poisson in distribution. The next characterization, is an extension of Watanabe’s theorem of characterization of homogeneous Poisson process. The last characterization will be illustrated by waiting time distributions, especially the matrix-exponential representation.

Suggested Citation

  • Huiming Zhang & Bo Li, 2016. "Characterizations of discrete compound Poisson distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(22), pages 6789-6802, November.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:22:p:6789-6802
    DOI: 10.1080/03610926.2014.901375
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    Cited by:

    1. Jing Luo & Haoyu Wei & Xiaoyu Lei & Jiaxin Guo, 2021. "Asymptotic in a class of network models with an increasing sub-Gamma degree sequence," Papers 2111.01301, arXiv.org, revised Nov 2023.
    2. Sakuma, Yutaka & Masuyama, Hiroyuki & Fukuda, Emiko, 2020. "A discrete-time single-server Poisson queueing game: Equilibria simulated by an agent-based model," European Journal of Operational Research, Elsevier, vol. 283(1), pages 253-264.
    3. Liron Ravner & Yutaka Sakuma, 2021. "Strategic arrivals to a queue with service rate uncertainty," Queueing Systems: Theory and Applications, Springer, vol. 97(3), pages 303-341, April.

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