Inequalities for Ek(X, Y) when the marginals are fixed
- Cite this article as:
- Cambanis, S., Simons, G. & Stout, W. Z. Wahrscheinlichkeitstheorie verw Gebiete (1976) 36: 285. doi:10.1007/BF00532695
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When k(x, y) is a quasi-monotone function and the random variables X and Y have fixed distributions, it is shown under some further mild conditions that ℰ k(X, Y) is a monotone functional of the joint distribution function of X and Y. Its infimum and supremum are both attained and correspond to explicitly described joint distribution functions.