## Bernoulli

- Bernoulli
- Volume 24, Number 1 (2018), 115-155.

### Maximum entropy distribution of order statistics with given marginals

Cristina Butucea, Jean-François Delmas, Anne Dutfoy, and Richard Fischer

#### Abstract

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.

#### Article information

**Source**

Bernoulli, Volume 24, Number 1 (2018), 115-155.

**Dates**

Received: September 2015

Revised: February 2016

First available in Project Euclid: 27 July 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1501142438

**Digital Object Identifier**

doi:10.3150/16-BEJ868

**Mathematical Reviews number (MathSciNet)**

MR3706752

**Zentralblatt MATH identifier**

06778323

**Keywords**

copula entropy maximum entropy order statistics

#### Citation

Butucea, Cristina; Delmas, Jean-François; Dutfoy, Anne; Fischer, Richard. Maximum entropy distribution of order statistics with given marginals. Bernoulli 24 (2018), no. 1, 115--155. doi:10.3150/16-BEJ868. https://projecteuclid.org/euclid.bj/1501142438