When Is the Conway-Maxwell-Poisson Distribution Infinitely Divisible?

Xi Geng; Aihua Xia

doi:10.1016/j.spl.2021.109264

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arXiv · 2011.04852

When Is the Conway-Maxwell-Poisson Distribution Infinitely Divisible?

Xi Geng·Aihua Xia

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Abstract

An essential character for a distribution to play a central role in the limit theory is infinite divisibility. In this note, we prove that the Conway-Maxwell-Poisson (CMP) distribution is infinitely divisible iff it is the Poisson or geometric distribution. This explains that, despite its applications in a wide range of fields, there is no theoretical foundation for the CMP distribution to be a natural candidate for the law of small numbers.

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Xi Geng, Aihua Xia. 2020-11-10. When Is the Conway-Maxwell-Poisson Distribution Infinitely Divisible?. https://doi.org/10.1016/j.spl.2021.109264

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