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Entropy Inequalities for Classes of Probability Distributions I. The Univariate Case

Samuel Karlin and Yosef Rinott
Advances in Applied Probability
Vol. 13, No. 1 (Mar., 1981), pp. 93-112
DOI: 10.2307/1426469
Stable URL: http://www.jstor.org/stable/1426469
Page Count: 20
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Entropy Inequalities for Classes of Probability Distributions I. The Univariate Case
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Abstract

Entropy functionals of probability densities feature importantly in classifying certain finite-state stationary stochastic processes, in discriminating among competing hypotheses, in characterizing Gaussian, Poisson, and other densities, in describing information processes, and in other contexts. Two general types of problems are considered. For a given parametric family of densities F, the member of maximal (or sometimes minimal) entropy is ascertained. Secondly, we determine a natural (partial) ordering over F for which the entropy functional is monotone. The examples include the multiparameter binomial, multiparameter negative binomial, some classes of log concave densities, and others.

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