On the optimal mapping of distributions

  • M. Knott
  • C. S. Smith
Contributed Papers


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 


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Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • M. Knott
    • 1
  • C. S. Smith
    • 1
  1. 1.Department of Statistical and Mathematical SciencesLondon School of Economics and Political ScienceLondonEngland

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