Extended inequalities for weighted Renyi entropy involving generalized Gaussian densities

TL;DR

This paper develops extended inequalities for weighted Renyi entropy and introduces generalized Gaussian densities, providing new bounds and relations in information theory.

Contribution

It introduces $ ext{ extalpha}$-th generalized derivation and ($ extalpha$; p)-th weighted Fisher information, extending classical inequalities to a weighted and generalized Gaussian context.

Findings

Derived extended moment-entropy inequalities

Established generalized Fisher information bounds

Provided new Cramer-Rao inequalities for weighted cases

Abstract

In this paper the author analyses the weighted Renyi entropy in order to derive several inequalities in weighted case. Furthermore, using the proposed notions $\alpha$-th generalized derivation and ($\alpha$; p)-th weighted Fisher information, extended versions of the moment-entropy, Fisher information and Cramer-Rao inequalities in terms of generalized Gaussian densities are given.