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|
|Pages (from-to)||339 - 351|
|Number of pages||13|
|Journal||Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques|
|Publication status||Published - 2007|