Ordering distributions by scaled order statistics
Résumé
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.
Domaines
Economie et sciences de la décision
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