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A generalized bivariate exponential distribution

Published online by Cambridge University Press:  14 July 2016

Albert W. Marshall  and
Ingram Olkin
Albert W. Marshall
Affiliation:
Boeing Scientific Research Laboratories
Ingram Olkin
Affiliation:
Stanford University
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Abstract

In a previous paper (Marshall and Olkin (1966)) the authors have derived a multivariate exponential distribution from points of view designed to indicate the applicability of the distribution. Two of these derivations are based on “shock models” and one is based on the requirement that residual life is independent of age.

The practical importance of the univariate exponential distribution is partially due to the fact that it governs waiting times in a Poisson process. In this paper, the distribution of joint waiting times in a bivariate Poisson process is investigated. There are several ways to define “joint waiting time”. Some of these lead to the bivariate exponential distribution previously obtained by the authors, but others lead to a generalization of it. This generalized bivariate exponential distribution is also derived from shock models. The moment generating function and other properties of the distribution are investigated.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 2 , August 1967 , pp. 291 - 302
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

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