Some results concerning maximum Renyi entropy distributions

OT Johnson, C Vignat

Research output: Contribution to journalArticle (Academic Journal)peer-review

29 Citations (Scopus)

Abstract

We consider the Student-t and Student-r distributions, which maximise RÃ©nyi entropy under a covariance condition. We show that they have information-theoretic properties which mirror those of the Gaussian distributions, which maximise Shannon entropy under the same condition. We introduce a convolution which preserves the RÃ©nyi maximising family, and show that the RÃ©nyi maximisers are the case of equality in a version of the Entropy Power Inequality. Further, we show that the RÃ©nyi maximisers satisfy a version of the heat equation, motivating the definition of a generalised Fisher information.
Translated title of the contribution Some results concerning maximum Renyi entropy distributions English 339 - 351 13 Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques 43 https://doi.org/10.1016/j.anihpb.2006.05.001 Published - 2007