Summary
For some subsets of the set of all Δ-monotone functions on [0,1] n we characterize distribution functions F, G such that E F f≦EG f for all f within these subsets. Furthermore, we determine sharp upper and lower bounds of integrals of functions in these subsets w.r.t. all distributions with fixed marginals and give some applications of these results.
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Rüschendorf, L. Inequalities for the expectation of Δ-monotone functions. Z. Wahrscheinlichkeitstheorie verw Gebiete 54, 341–349 (1980). https://doi.org/10.1007/BF00534351
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DOI: https://doi.org/10.1007/BF00534351