Ordering Distributions by Scaled Order Statistics.
ARIZONA UNIV TUCSON DEPT OF MATHEMATICS
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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.
- Statistics and Probability