Year: 2019
Type: article
Abstract: Rényi's information measures-the Rényi information, mean, capacity, radius, and center-are analyzed relying on the elementary properties of the Rényi divergence and the power means. The van Erven- Harremoës conjecture is proved for any positive order and for any set of probability measures on a given measurable space and a generalization of it is established for the constrained variant of the problem. The finiteness of the order Rényi capacity is shown to imply the continuity of the Rényi capacity on (0, α] and the uniform equicontinuity of the Rényi information, both as a family of functions of the order indexed by the priors and as a family of functions of the prior indexed by the orders.
Author: Baris Nakiboglu
Institution: Middle East Technical University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2767710368