When Is the Conway-Maxwell-Poisson Distribution Infinitely Divisible?
Probability
2023-02-27 v1
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.
Keywords
Cite
@article{arxiv.2011.04852,
title = {When Is the Conway-Maxwell-Poisson Distribution Infinitely Divisible?},
author = {Xi Geng and Aihua Xia},
journal= {arXiv preprint arXiv:2011.04852},
year = {2023}
}
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11 pages