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

Research output: Contribution to journalArticle (Academic Journal)peer-review

44 Citations (Scopus)

Abstract

We prove that the Poisson distribution maximises entropy in the class of ultra log-concave distributions, extending a result of Harremo\"{e}s. 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.
Translated title of the contributionLog-concavity and the maximum entropy property of the Poisson distribution
Original languageEnglish
Pages (from-to)791 - 802
Number of pages12
JournalStochastic Processes and their Applications
Volume117 (6)
DOIs
Publication statusPublished - Jun 2007

Bibliographical note

Publisher: Elsevier

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