Contributed Papers

Journal of Optimization Theory and Applications

, Volume 43, Issue 1, pp 39-49

First online:

On the optimal mapping of distributions

  • M. KnottAffiliated withDepartment of Statistical and Mathematical Sciences, London School of Economics and Political Science
  • , C. S. SmithAffiliated withDepartment of Statistical and Mathematical Sciences, London School of Economics and Political Science

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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

Inequalities marginal distributions Fréchet derivatives