Log-concavity and the maximum entropy property of the Poisson distribution
Probability
2010-08-17 v2
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.
Keywords
Cite
@article{arxiv.math/0603647,
title = {Log-concavity and the maximum entropy property of the Poisson distribution},
author = {Oliver Johnson},
journal= {arXiv preprint arXiv:math/0603647},
year = {2010}
}
Comments
16 pages: revised version, accepted by Stochastic Processes and their Applications