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On the optimal mapping of distributions

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

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 

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References

  1. 1.
    Tchen, A. H.,Inequalities for Distributions with Given Marginals, Annals of Probability, Vol. 8, pp. 814–827, 1980.Google Scholar
  2. 2.
    Berge, C., andGhouila-Houri, A.,Programming, Games, and Transportation Networks, Methuen and Company, London, England, 1965.Google Scholar
  3. 3.
    Monge, G.,Deblai et Remblai, Mémoires de l'Académie des Sciences, 1781.Google Scholar
  4. 4.
    Appell, P.,Le Problème Géométrique des Déblais et Remblais, Mémorial des Sciences Mathématiques, Vol. 27, pp. 1–34, 1928.Google Scholar
  5. 5.
    Appell, P.,Sur un Théorème de Monge et sur une Généralization de Ce Théorème, Acta Mathematica, Vol. 47, pp. 7–14, 1926.Google Scholar

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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