A MULTIVARIATE EXPONENTIAL DISTRIBUTION

Abstract

A number of multivariate exponential distributions are known, but they have not been obtained by methods that shed light on their applicability. This paper presents some meaningful derivations of a multivariate exponential distribution that serve to indicate conditions under which the distribution is appropriate. Two of these derivations are based on 'shock models', and one is based on the requirement that residual life is independent of age. It is significant that the derivations all lead to the same distribution. For this distribution, the moment generating function is obtained, comparison is made with the case of independence, the distribution of the minimum is discussed, and various other properties are investigated. A multivariate gamma distribution is obtained by convolution, and a multivariate Weibull distribution is obtained through a change of variables.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1966
Accession Number
AD0634335

Entities

People

  • Albert W. Marshall
  • Ingram Olkin

Organizations

  • Boeing

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Convolution
  • Distribution Functions
  • Equations
  • Geiger Counters
  • Jet Engines
  • Mathematics
  • Probability
  • Random Variables
  • Reliability
  • Residuals
  • Scientific Research
  • Statistics
  • Survival
  • Transitions
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Mechanical Engineering/Mechanics of Materials.
  • Statistical inference.