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On a characterization of the exponential distribution by order statistics

Published online by Cambridge University Press:  14 July 2016

M. Ahsanullah
M. Ahsanullah*
Affiliation:
Empresa Brasileira de Pequisa Agropecuária (EMBRAPA), Brasília, D.F.
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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 the identical distribution of the random variables nX1,n and (n − i + 1)(X1,n −; Xi–1,n) for one i and one n with 2 ≦ i ≦ n.

Keywords

EXPONENTIAL DISTRIBUTIONCHARACTERIZATIONIDENTICAL DISTRIBUTIONABSOLUTELY CONTINUOUSMONOTONE HAZARD RATEORDER STATISTICSNONNEGATIVE RANDOM VARIABLE
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 818 - 822
Copyright
Copyright © Applied Probability Trust 1976 

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