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Multivariate exponential distributions based on hierarchical successive damage

Published online by Cambridge University Press:  14 July 2016

Barry C. Arnold
Barry C. Arnold*
Affiliation:
Iowa State University, Ames
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Abstract

A class of multivariate exponential distributions is suggested which includes those presented by Marshall and Olkin, Downton, and Hawkes. It is based on a concept of hierarchical successive damage. Recursive expressions for the Laplace transforms and for first and second moments are derived in the bivariate case. Related multivariate geometric distributions are described.

Keywords

MULTIVARIATEEXPONENTIALGEOMETRICSHOCK MODEL
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 142 - 147
Copyright
Copyright © Applied Probability Trust 1975 

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References

Arnold, B. C. (1974) A characterization of the exponential distribution by multivariate geometric compounding. Sankhya. To appear.Google Scholar
Downton, F. (1970) Bivariate exponential distributions in reliability theory. J. R. Statist. Soc. B 32, 408–417.Google Scholar
Hawkes, A. G. (1972) A bivariate exponential distribution with applications to reliability. J. R. Statist. Soc. B 34, 129–131.Google Scholar
Marshall, A. W. and Olkin, I. (1967) A multivariate exponential distribution. J. Amer. Statist. Ass. 62, 30–44.CrossRefGoogle Scholar
Paulson, A. S. and Uppuluri, V. R. R. (1972) A characterization of the geometric distribution and a bivariate geometric distribution. Sankhya Ser. A 34, 297–300.Google Scholar