Information-theoretic inequalities for contoured probability distributions

Authors:
O. G. Guleryuz;E. Lutwak;Deane Yang;Gaoyong Zhang
Affiliations:
Dept. of Math., Polytech. Univ. Brooklyn, NY;-;-;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

We show that for a special class of probability distributions that we call contoured distributions, information-theoretic invariants and inequalities are equivalent to geometric invariants and inequalities of bodies in Euclidean space associated with the distributions. Using this, we obtain characterizations of contoured distributions with extremal Shannon and Renyi entropy. We also obtain a new reverse information-theoretic inequality for contoured distributions.