The Annals of Mathematical Statistics

A Theorem on Factorial Moments and Its Applications

P. V. Krishna Iyer

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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.

Article information

Source
Ann. Math. Statist., Volume 29, Number 1 (1958), 254-261.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177706723

Digital Object Identifier
doi:10.1214/aoms/1177706723

Mathematical Reviews number (MathSciNet)
MR93841

Zentralblatt MATH identifier
0089.15503

JSTOR
links.jstor.org

Citation

Iyer, P. V. Krishna. A Theorem on Factorial Moments and Its Applications. Ann. Math. Statist. 29 (1958), no. 1, 254--261. doi:10.1214/aoms/1177706723. https://projecteuclid.org/euclid.aoms/1177706723


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Corrections

  • See Correction: P. V. Krishna Iyer. Correction Notes: Corrections to "A Theorem on Factorial Moments and Its Applications". Ann. Math. Statist., Volume 32, Number 2 (1961), 620--620.