A characterization by linearity of the regression function based on order statistics

We consider an infinite sequence X1,X2,... of independent random variables having a common continuous distribution function F(x). For 1[less-than-or-equals, slant]i[less-than-or-equals, slant]n, let {Xi:n} denote the ith order statistic among X1,...,Xn. In this paper, we characterize the distributions for which the regression E((X1:n+...+Xn:n)/nXk:n=x) is a linear function of x.

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Year of publication:	2003
Authors:	Balakrishnan, N. ; Akhundov, I. S.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 63.2003, 4, p. 435-440
Publisher:	Elsevier
Subject:	Order statistics Regression function Characterization

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

Persistent link: https://www.econbiz.de/10005259271