Inequalities for Ek(X, Y) when the marginals are fixed

  • Stamatis Cambanis
  • Gordon Simons
  • William Stout
Article

DOI: 10.1007/BF00532695

Cite this article as:
Cambanis, S., Simons, G. & Stout, W. Z. Wahrscheinlichkeitstheorie verw Gebiete (1976) 36: 285. doi:10.1007/BF00532695

Abstract

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.

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Stamatis Cambanis
    • 1
  • Gordon Simons
    • 1
  • William Stout
    • 2
  1. 1.Department of StatisticsUniversity of North CarolinaChapel HillUSA
  2. 2.Department of MathematicsUniversity of IllinoisChampaign-UrbanaUSA