A GENERALIZED BIVARIATE EXPONENTIAL DISTRIBUTION

Abstract

In a previous paper ('A Multivariate Exponential Distribution,' AD- 634 335) 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 bases 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.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1966
Accession Number
AD0644120

Entities

People

  • Albery W. Marshall
  • Ingram Olkin

Organizations

  • Boeing

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Bernoulli Distribution
  • Differential Equations
  • Distribution Functions
  • Equations
  • Integrals
  • Mathematics
  • Probability
  • Random Variables
  • Scientific Research
  • Survival

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Systems Analysis and Design