Information-theoretic inequalities for contoured probability distributions


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.

DOI: 10.1109/TIT.2002.800496

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@article{Guleryuz2002InformationtheoreticIF, title={Information-theoretic inequalities for contoured probability distributions}, author={Onur G. Guleryuz and Erwin Lutwak and Deane Yang and Gaoyong Zhang}, journal={IEEE Trans. Information Theory}, year={2002}, volume={48}, pages={2377-2383} }