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A characterization of the exponential distribution

Published online by Cambridge University Press:  14 July 2016

M. Ahsanullah  and
M. Rahman
M. Ahsanullah
Affiliation:
Food and Drug Directorate, Ottawa
M. Rahman
Affiliation:
Carleton University, Ottawa
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Abstract

A necessary and sufficient condition based on order statistics that a positive random variable having an absolutely continuous probability distribution (with respect to Lebesgue measure) will be exponential is given.

Keywords

CHARACTERIZATION OF EXPONENTIAL DISTRIBUTIONORDER STATISTICS
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 457 - 461
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Aczel, J. (1966) Lectures on Functional Equations and their Application. Academic Press, New York.Google Scholar
[2] Arnold, B. C. (1971) Two characterizations of the exponential distribution using order statistics. Unpublished.Google Scholar
[3] Basu, A. P. (1965) On characterizing the exponential distribution by order statistics. Ann. Inst. Statist. Math. 17, 93–96.Google Scholar
[4] Crawford, G. B. (1966) Characterization of geometric and exponential distributions. Ann. Math. Statist. 37, 1790–1795.Google Scholar
[5] Desu, M. M. (1971) A characterization of the exponential distribution by order statistics. Ann. Math. Statist. 42, 837–838.Google Scholar
[6] Ferguson, T. S. (1964) A characterization of the exponential distribution. Ann. Math. Statist. 35, 1199–1207.Google Scholar