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

Oliver Johnson

Stochastic Processes and their Applications, 2007, vol. 117, issue 6, 791-802

Abstract: 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.

Keywords: Log-concavity; Maximum; entropy; Poisson; distribution; Thinning; Ultra; log-concavity (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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