Journal of Optimization Theory and Applications

, Volume 43, Issue 1, pp 39–49

On the optimal mapping of distributions

Authors

  • M. Knott
    • Department of Statistical and Mathematical SciencesLondon School of Economics and Political Science
  • C. S. Smith
    • Department of Statistical and Mathematical SciencesLondon School of Economics and Political Science
Contributed Papers

DOI: 10.1007/BF00934745

Cite this article as:
Knott, M. & Smith, C.S. J Optim Theory Appl (1984) 43: 39. doi:10.1007/BF00934745

Abstract

We consider the problem of mappingXY, whereX andY have given distributions, so as to minimize the expected value of ∣XY2. This is equivalent to finding the joint distribution of the random variable (X, Y), with specified marginal distributions forX andY, such that the expected value of ∣XY2 is minimized. We give a sufficient condition for the minimizing joint distribution and supply numerical results for two special cases.

Key Words

Inequalitiesmarginal distributionsFréchet derivatives

Copyright information

© Plenum Publishing Corporation 1984