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Record values and the exponential distribution

Published online by Cambridge University Press:  14 July 2016

A. C. Dallas
A. C. Dallas*
Affiliation:
University of Athens
*
∗ Postal address: Statistical Unit, University of Athens, Panepistemiopolis, Athens 621, Greece.
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Abstract

Let X 1, X 2, · ·· be i.i.d. and Yk = max{X 1, X 2, · ··, X k}. Then Xj is a record value of the sequence if Yj > Yj -1). Denoting record value times by Ln, n = 1, 2, ···, we prove that the independence of XLj − XLi and XLi with Lj > characterizes the exponential distribution.

Keywords

RECORDSINDEPENDENCECHARACTERIZATIONEXPONENTIAL DISTRIBUTION

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 949 - 951
Copyright
Copyright © Applied Probability Trust 1981 

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References

Ahsanullah, M. (1978) Record values and the exponential distribution. Ann. Inst. Statist. Math. 30, 429–433.CrossRefGoogle Scholar
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Srivastava, R. C. (1978) Some characterizations of the exponential distribution based on record values (abstract). Bull I.M.S. 7, 283.Google Scholar
Tata, M. N. (1969) On outstanding values in a sequence of random variables. Z. Wahrscheinlichkeitsth. 12, 9–20.Google Scholar