A criterion for the compound Poisson distribution to be maximum entropy

Authors:
Oliver Johnson;Ioannis Kontoyiannis;Mokshay Madiman
Affiliations:
Department of Mathematics, University of Bristol, University Walk, Bristol, UK;Department of Informatics, Athens University of Economics & Business, Athens, Greece;Department of Statistics, Yale University, New Haven, CT
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Year:
2009

Citing 4
Cited 0

Binomial and Poisson distributions as maximum entropy distributions

IEEE Transactions on Information Theory
Entropy and the law of small numbers

IEEE Transactions on Information Theory
Monotonic Decrease of the Non-Gaussianness of the Sum of Independent Random Variables: A Simple Proof

IEEE Transactions on Information Theory
Generalized Entropy Power Inequalities and Monotonicity Properties of Information

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

The Poisson distribution is known to have maximal entropy among all distributions (on the nonnegative integers) within a natural class. Interestingly, straight forward attempts to generalize this result to general compound Poisson distributions fail because the analogous result is not true in general. However, we show that the compound Poisson does indeed have a natural maximum entropy characterization when the distributions under consideration are log-concave. This complements the recent development by the same authors of an information-theoretic foundation for compound Poisson approximation inequalities and limit theorems.