Log-concavity and the maximum entropy property of the Poisson distribution

We prove that the Poisson distribution maximises entropy in the class of ultra log-concave distributions, extending a result of Harremoës. The proof uses ideas concerning log-concavity, and a semigroup action involving adding Poisson variables and thinning. We go on to show that the entropy is a concave function along this semigroup.

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Year of publication:	2007
Authors:	Johnson, Oliver
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 117.2007, 6, p. 791-802
Publisher:	Elsevier
Keywords:	Log-concavity Maximum entropy Poisson distribution Thinning Ultra log-concavity

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008873933