Abstract
The theorem that the $s$th factorial moment for the sum of $N$ events is $s!$ times the sum of the expectations for any $s$ of the events occurring simultaneously has been proved by induction. The applications of this result in obtaining easily the moments of a number of distributions arising from a sequence of observations belonging to two continuous populations and other cases have been demonstrated.
Citation
P. V. Krishna Iyer. "A Theorem on Factorial Moments and Its Applications." Ann. Math. Statist. 29 (1) 254 - 261, March, 1958. https://doi.org/10.1214/aoms/1177706723
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