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- W2026257356 abstract "Let X ( ω ) be a random element taking values in a linear space X endowed with the partial order ≤; let G 0 be the class of nonnegative order-preserving functions on X such that, for each g∈ G 0 , E [ g ( X )] is defined; and let G 1 ņ G 0 be the subclass of concave functions. A version of Markov's inequality for such spaces in P(X ≥ x) ≤ inf G 0 E[g(X)]/g(x) . Moreover, if E ( X ) = ξ is defined and if Jensen's inequality applies, we have a further inequality P(X≥x) ≤ inf G 1 E[g(X)]/g(x) ≤ inf G 1 g(ξ)/g(x) . Applications are given using a variety or orderings of interest in statistics and applied probability." @default.
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- W2026257356 date "1981-06-01" @default.
- W2026257356 modified "2023-09-30" @default.
- W2026257356 title "Markov inequalities on partially ordered spaces" @default.
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- W2026257356 doi "https://doi.org/10.1016/0047-259x(81)90112-3" @default.
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