On the entropy of compound distributions on nonnegative integers

Authors:
Yaming Yu
Affiliations:
Department of Statistics, University of California, Irvine, CA
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

Some entropy comparison results are presented concerning compound distributions on nonnegative integers. The main result shows that, under a log-concavity assumption, two compound distributions are ordered in terms of Shannon entropy if both the "numbers of claims" and the "claim sizes" are ordered accordingly in the convex order. Several maximum/minimum entropy theorems follow as a consequence. Most importantly, two recent results of Johnson et al. (2008) on maximum entropy characterizations of compound Poisson and compound binomial distributions are proved under fewer assumptions and with simpler arguments.