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

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

2006-03-28

arxiv.org/abs/math/0603647v2

Stochastic Processes and their Applications, Vol 117/6, 2007, pages 791-802

Mathematics

Probability

16 pages: revised version, accepted by Stochastic Processes and their Applications

Scientific paper

10.1016/j.spa.2006.10.006

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.

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