Factorial moments of the Poisson distribution of order $k$

S. R. Mane

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arXiv · 2311.15184

Factorial moments of the Poisson distribution of order $k$

S. R. Mane

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Abstract

The factorial moments of the standard Poisson distribution are well known. The present note presents an explicit combinatorial sum for the factorial moments of the Poisson distribution of order $k$. Unlike the standard Poisson distribution (the case $k=1$), for $k>1$ the structure of the factorial moments is much more complicated. Some properties of the factorial moments of the Poisson distribution of order $k$ are elucidated in this note.

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S. R. Mane. 2023-11-26. Factorial moments of the Poisson distribution of order $k$. https://arxiv.org/abs/2311.15184

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