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 Rényi 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 Rényi maximising family, and show that the Rényi maximisers are the case of equality in a version of the Entropy Power Inequality. Further, we show that the Rényi maximisers satisfy a version of the heat equation, motivating the definition of a generalised Fisher information.
Translated title of the contributionSome results concerning maximum Renyi entropy distributions
Original languageEnglish
Pages (from-to)339 - 351
Number of pages13
JournalAnnales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Volume43
DOIs
Publication statusPublished - 2007

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