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

Oliver Johnson
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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.

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Oliver Johnson. 2006-10-11. Log-concavity and the maximum entropy property of the Poisson distribution. https://doi.org/10.1016/j.spa.2006.10.006

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