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Ordering distributions by scaled order statistics

Abstract : Motivated by applications in reliability theory, we define a preordering (X sub 1, ..., X sub n) about or less than (k) (Y sub 1, ..., Y sub n) of nonnegative random vectors by requiring the k-th order statistic of a sub 1 X sub 1, ..., a sub n X sub n to be stochastically smaller than the k-th order statistic of a sub 1 Y sub 1, ..., a sub n Y sub n for all choices of a sub i > O, i = 1, 2, ..., n. We identify a class of functions M sub k, n such that X about or less than (k) Y if and only if E phi (X) < E phi (Y) for all phi epsilon M sub k,n. Some preservation results related to the ordering about or less than (k) are obtained. Some examples and applications of the results are given.
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Contributor : Antoine Haldemann <>
Submitted on : Thursday, December 2, 2010 - 9:54:52 AM
Last modification on : Thursday, January 11, 2018 - 6:19:31 AM

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Marco Scarsini, Moshe Shaked. Ordering distributions by scaled order statistics. Mathematical Methods of Operations Research, Springer Verlag, 1987, Vol. 31, N°1, pp. A1-A13. ⟨10.1007/BF01258603⟩. ⟨hal-00542242⟩



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