The Minimum of the Entropy of a Two-Dimensional Distribution with Given Marginals
Giorgio Dall’Aglio, Elisabetta Bona · arXiv (Cornell University) · 2011
The paper search for the minimum of the entropy of a two- dimensional distribution in the Fréchet class, the class of distributions with given marginals. The main result for discrete distributions is an algorithm for building the minimizing distribution, which is given by the maximum distribution function of the Fréchet class after a suitable rearrangement of the rows and of the columns. For absolutely continuous distributions a minimum does not exists, and the infimum is equal to -\infty.