On the optimal mapping of distributions |
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Authors: | M Knott C S Smith |
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Institution: | (1) Department of Statistical and Mathematical Sciences, London School of Economics and Political Science, London, England |
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Abstract: | We consider the problem of mappingX Y, whereX andY have given distributions, so as to minimize the expected value of X–Y 2. 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 X–Y 2 is minimized. We give a sufficient condition for the minimizing joint distribution and supply numerical results for two special cases. |
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Keywords: | Inequalities marginal distributions Fré chet derivatives |
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