Title :
A Geometric Characterization of Maximum Rényi Entropy Distributions
Author :
Vignat, Christophe ; Hero, Alfred O. ; Costa, José A.
Author_Institution :
LPM, Ecole Polytech. Fed. de Lausanne
Abstract :
In this paper, we provide a detailed geometric characterization of multivariate distributions that maximize Renyi entropy under covariance constraint. These distributions are shown to be marginals of the uniform distribution on the hypersphere for q > 1, and conditional distributions of projections of this uniform distribution in the case q > 1. This construction allows to build a natural convolution of random type for which these distributions are stable
Keywords :
geometry; maximum entropy methods; covariance constraint; geometric characterization; maximum Renyi entropy distributions; multivariate distributions; Convergence; Convolution; Covariance matrix; Entropy; Gaussian distribution; Mathematics; Random variables; Stochastic processes; Symmetric matrices; USA Councils;
Conference_Titel :
Information Theory, 2006 IEEE International Symposium on
Conference_Location :
Seattle, WA
Print_ISBN :
1-4244-0505-X
Electronic_ISBN :
1-4244-0504-1
DOI :
10.1109/ISIT.2006.261749
