On the Distribution of Products of Random Variables

1 September 1967

journal article
research article
Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology

Vol. 29 (3) , 513-524
https://doi.org/10.1111/j.2517-6161.1967.tb00713.x

Abstract

The problem of finding the probability density function of the product of n identically distributed independent normal variables was solved by Springer and Thompson (1966). Their formulae for n ≤ 7 are simplified in this paper and generalized to an arbitrary number of factors. Similar formulae for the corresponding probability distribution functions are derived. The applicability of these results to the cases of the negative exponential, Weibull and gamma distributions is discussed.

Keywords

This publication has 3 references indexed in Scilit:

The Distribution of Products of Independent Random Variables
SIAM Journal on Applied Mathematics, 1966
On random variables whose quotient follows the Cauchy law
Colloquium Mathematicum, 1959
Some Applications of the Mellin Transform in Statistics
The Annals of Mathematical Statistics, 1948