On a characterization of the exponential distribution by properties of order statistics
type: Item
instance of: scholarly article
title: On a characterization of the exponential distribution by properties of order statistics
zbMATH Open document ID: 0655.62008
DOI: 10.1016/0167-7152(88)90032-6
author: Ursula Gather
published in: Statistics \& Probability Letters
publication date: 1988-01-01T00:00:00Z
review text: A continuous c.d.f. F(x), strictly increasing for \(x>0\), is exponential if and only if \(X_{j,n}-X_{i,n}\) and \(X_{j-i,n-i}\) have identical distributions for some i,n, \(j=j_ 1,j_ 2\), \(1\leq i<j_ 1<j_ 2\leq n\), \(n\geq 3\). A new proof of this characterization is given, since in \textit{M. Ahsanullah}'s paper in G. P. Patil, S. Kotz and J. K. Ord (eds.), A modern course on statistical distributions in scientific work. Vol. 3. NATO Advanced Study Institutes Series. Ser. C (1975; Zbl 0308.60003), p. 131-135, where it was stated first, an implicit assumption in the proof is that F is NBU or NWU.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 62E15
zbMATH DE Number: 4070020
zbMATH Keywords: exponential distribution
zbMATH Keywords: order statistics
zbMATH Keywords: characterization
zbMATH Keywords: NBU
zbMATH Keywords: NWU
MaRDI profile type: Publication
full work available at URL: 0167-7152(88)90032-6
OpenAlex ID: W2003018724
cites work: On a characterization of the exponential distribution by order statistics
cites work: A characterization of the exponential distribution by higher order gap
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cites work: Characterizations of probability distributions. A unified approach with an emphasis on exponential and related models
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cites work: Characterization of the exponential and the pareto distributions by means of some properties of the distributions which the differences and quotients of order statistics are subject to
description: scientific article; zbMATH DE number 4070020