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A characterization of the exponential distribution by spacings

Published online by Cambridge University Press:  14 July 2016

M. Ahsanullah
M. Ahsanullah*
Affiliation:
Health Protection Branch, Health and Welfare Canada, Ottawa
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Abstract

Let X1, X2, ···, Xn be a random sample of size n from a population with probability density function f(x), x > 0, and let X1, n < X2, n < ··· < Xn, n be the associated order statistics. A characterization of the exponential distribution is shown by considering identical distribution of the random variables (n − i + 1)(Xi, n − Xi−1, n) and (n − i)(Xi+1, n − Xi, n) for one i and one n with 2 ≦ i ˂ n.

Keywords

EXPONENTIAL DISTRIBUTIONCHARACTERIZATIONSPACINGSIDENTICAL DISTRIBUTIONSABSOLUTELY CONTINUOUSMONOTONE HAZARD RATEORDER STATISTICSNON-NEGATIVE RANDOM VARIABLE
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 650 - 653
Copyright
Copyright © Applied Probability Trust 1978 

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References

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