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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 X1, X2, · ·· be i.i.d. and Yk = max{X1, X2, · ··, Xk}. 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
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
Galambos, J. and Kotz, S. (1978) Characterizations of Probability Distributions. Lecture Notes in Mathematics 675, Springer-Verlag, Berlin.Google Scholar
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