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A Theorem on Factorial Moments and Its Applications
P. V. Krishna Iyer
The Annals of Mathematical Statistics
Vol. 29, No. 1 (Mar., 1958), pp. 254-261
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2237312
Page Count: 8
You can always find the topics here!Topics: Mathematical moments, Factorials, Population distributions, Mathematical sequences
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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.
The Annals of Mathematical Statistics © 1958 Institute of Mathematical Statistics