Open Access
February 2018 Maximum entropy distribution of order statistics with given marginals
Cristina Butucea, Jean-François Delmas, Anne Dutfoy, Richard Fischer
Bernoulli 24(1): 115-155 (February 2018). DOI: 10.3150/16-BEJ868


We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we give explicitly the density of the unique distribution which achieves the maximal entropy and compute the value of its entropy. This density is the unique one which has a product form on its support and the given one-dimensional marginals. The proof relies on the study of copulas with given one-dimensional marginal distributions for its order statistics.


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Cristina Butucea. Jean-François Delmas. Anne Dutfoy. Richard Fischer. "Maximum entropy distribution of order statistics with given marginals." Bernoulli 24 (1) 115 - 155, February 2018.


Received: 1 September 2015; Revised: 1 February 2016; Published: February 2018
First available in Project Euclid: 27 July 2017

zbMATH: 06778323
MathSciNet: MR3706752
Digital Object Identifier: 10.3150/16-BEJ868

Keywords: copula , Entropy , maximum entropy , order statistics

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 1 • February 2018
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