CHARACTERIZATIONS OF THE WEIBULL DISTRIBUTION BY THE INDEPENDENCE OF THE UPPER RECORD VALUES

Chang, Se-Kyung; Chang, Se-Kyung; Lee, Min-Young; Lee, Min-Young

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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Vol.15 No.2

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CHARACTERIZATIONS OF THE WEIBULL DISTRIBUTION BY THE INDEPENDENCE OF THE UPPER RECORD VALUES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2008, v.15 no.2, pp.163-167

Chang, Se-Kyung
Lee, Min-Young

Chang,, S. , & Lee,, M. (2008). CHARACTERIZATIONS OF THE WEIBULL DISTRIBUTION BY THE INDEPENDENCE OF THE UPPER RECORD VALUES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 15(2), 163-167.

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Abstract

This paper presents characterizations of the Weibull distribution by the independence of record values. We prove that <TEX>$X\;{\in}\;W\;EI ({\alpha})$</TEX>, if and only if <TEX>$\frac {X_{U(n+l)}} {X_{U(n+1)}\;+\;X_{U(n)}}$</TEX> and <TEX>$X_{U(n+1)}$</TEX> for <TEX>$n{\geq}1$</TEX> are independent or <TEX>$\frac {X_{U(n)}} {X_{U(n+1)}\;+\;X_{U(n)}}$</TEX> and <TEX>$X_{U(n+1)}$</TEX> for <TEX>$n{\geq}1$</TEX> are independent. And also we establish that <TEX>$X\;{\in}\;W\;EI({\alpha})$</TEX>, if and only if <TEX>$\frac {X_{U(n+1)}\;-\;X_{U(n)}} {X_{U(n+1)}\;+\;X_{U(n)}}$</TEX> and <TEX>$X_{U(n+1)}$</TEX> for <TEX>$n{\geq}1$</TEX> are independent.

keywords: record values, characterization, independence, Weibull distribution

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Article Contents

Vol.15 No.2

CHARACTERIZATIONS OF THE WEIBULL DISTRIBUTION BY THE INDEPENDENCE OF THE UPPER RECORD VALUES

Abstract

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics