On a characterization of the exponential distribution by properties of order statistics

A continuous c.d.f. F(x), strictly increasing for x> 0, is exponential if and only if Xj, n - Xi, n and Xj-i, n-i have identical distribution for some i, n, J = j1, j2, 1 [less-than-or-equals, slant] i < j1 <j2 [less-than-or-equals, slant] n, n [greater-or-equal, slanted] 3. A new proof of this characterization is given, since in Ahsanullah (1975) where it was stated first, an implicit assumption in the proof is that F is NBU or NWU.

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Year of publication:	1988
Authors:	Gather, Ursula
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 7.1988, 2, p. 93-96
Publisher:	Elsevier
Subject:	exponential distribution characterization order statistics

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005223037