On a characterization of the exponential distribution by spacings

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1978 English Publisher:Springer Science and Business Media LLCJournal:Annals of the Institute of Statistical Mathematics, volume 30 (issn: 0020-3157, eissn: 1572-9052,

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Authors: Ahsanullah, M.;

doi: 10.1007/bf02480209 , 10.2307/3213130 , 10.1007/bf02932470 , 10.1017/s0021900200046040

On a characterization of the exponential distribution by spacings

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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

Reliability and life testing, order statistics, characterization of exponential distribution, spacings, Characterization and structure theory of statistical distributions, Order statistics; empirical distribution functions

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