Characterizations of identically distributed independent random variables using order statistics

Suppose X1,...Xn are independent random variables of continuous type with proportional hazard (or failure) rates. Let X(r) denote the rth order statistic and let I(r) = i if Xi = X(r). It is proved that Xi's are identically distributed if and only if X(r) and I(r) are independent for some r [set membership, variant] {2,...,n}. The second characterization is in terms of order statistics from subsamples.

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Year of publication:	1993
Authors:	Bapat, R. B. ; Kochar, Subhash C.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 17.1993, 3, p. 225-230
Publisher:	Elsevier
Keywords:	Order statistics hazard rate competing risks

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

Persistent link: https://www.econbiz.de/10005259168