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- W2045249719 abstract "Motivated by applications in reliability theory, we define a preordering (X 1, ...,X n) $$mathop lesssim limits^{{text{(}}k)}$$ (Y 1 ...,Y n) of nonnegative random vectors by requiring thek-th order statistic ofa 1 X 1,..., a n X n to be stochastically smaller than thek-th order statistic ofa 1 Y 1, ...,a n Y n for all choices ofa i >0,i=1, 2, ...,n. We identify a class of functionsM k, n such that $$Xmathop lesssim limits^{{text{(}}k)} Y$$ if and only ifEφ(X)⩽Eφ(Y) for allφεM k,n. Some preservation results related to the ordering $$mathop lesssim limits^{{text{(}}k)}$$ are obtained. Some applications of the results in reliability theory are given." @default.
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- W2045249719 date "1987-01-01" @default.
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- W2045249719 title "Ordering distributions by scaled order statistics" @default.
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- W2045249719 doi "https://doi.org/10.1007/bf01258603" @default.
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