Ordering distributions by scaled order statistics

Marco Scarsini and Moshe Shaked ()
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Moshe Shaked: University of Arizona

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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)

Keywords: Reliability; Order statistics; Lifetime; Stochastic orderings (search for similar items in EconPapers)
Date: 1987
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Published in Mathematical Methods of Operations Research, 1987, Vol. 31, N°1, pp. A1-A13. ⟨10.1007/BF01258603⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00542242

DOI: 10.1007/BF01258603

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