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 1ņ 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.
Published Version
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