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 contribution | Log-concavity and the maximum entropy property of the Poisson distribution |
|---|---|
| Original language | English |
| Pages (from-to) | 791 - 802 |
| Number of pages | 12 |
| Journal | Stochastic Processes and their Applications |
| Volume | 117 (6) |
| DOIs | |
| Publication status | Published - Jun 2007 |