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Characterization of a general class of life-testing models

Part of: Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

M. E. Ghitany ,
M. A. El-saidi  and
Z. Khalil
M. E. Ghitany*
Affiliation:
Kuwait University
M. A. El-saidi*
Affiliation:
Ferris State University
Z. Khalil*
Affiliation:
Concordia University
*
∗Postal address: Department of Statistics and Operations Research, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait.
∗∗Postal address: Ferris State University, Big Rapids, Michigan 49307, U.S.A.
∗∗∗Postal address: Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec, Canada, H4B 1R6.
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Abstract

In this paper we establish a characterization theorem for a general class of life-testing models based on a relationship between conditional expectation and the failure rate function. As a simple application of the theorem, we characterize the gamma, Weibull, and Gompertz distributions, since they have many probabilistic and statistical properties useful in both biometry and engineering reliability.

Keywords

CONDITIONAL EXPECTATIONHAZARD FUNCTIONSURVIVAL FUNCTIONBIOMETRYRELIABILITY

MSC classification

Primary: 60E05: Distributions
Secondary: 62E10: Characterization and structure theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 548 - 553
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

∗

On sabbatical leave at Kuwait University.

References

Azlarov, T. and Volodin, N. (1986) Characterization Problems Associated with the Exponential Distribution. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Dimitrov, B. and Khalil, Z. (1990) On a new characterizing property of the exponential distribution. J. Appl. Prob. 27, 221–226.CrossRefGoogle Scholar
Galambos, J. and Kotz, S. (1978) Characterizations of Probability Distributions; A Unified Approach with an Emphasis on Exponential and Related Models. Lecture Notes in Mathematics 675, Springer-Verlag, Berlin.Google Scholar
Johnson, N. L. and Kotz, S. (1970) Distributions in Statistics: Continuous Univariate Distributions 1. Wiley, New York.Google Scholar
Koicheva, M. (1993) A characterization of the gamma distribution in terms of conditional moments. Appl. Math. 38, 19–22.CrossRefGoogle Scholar
Letac, J. (1985) A characterization of the gamma distribution. Adv. Appl. Prob. 17, 911–912.CrossRefGoogle Scholar