Factorial moments of the Poisson distribution of order k
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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