## The Annals of Mathematical Statistics

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

### A Theorem on Factorial Moments and Its Applications

#### 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

#### 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.Project Euclid: euclid.aoms/1177705075