Results on the solutions of maximum weighted Renyi entropy problems

TL;DR

This paper analyzes the maximum weighted Renyi entropy problem, demonstrating that Student-r and Student-t distributions maximize the entropy under certain weight constraints, and extends the Hadamard inequality.

Contribution

It identifies the maximizing distributions for weighted Renyi entropy and extends a classical inequality under new conditions.

Findings

Student-r and Student-t distributions maximize weighted Renyi entropy under specific constraints

Extended version of the Hadamard inequality derived

Provides theoretical insights into entropy maximization with weights

Abstract

In this paper, following standard arguments, the maximum Renyi entropy problem for the weighted case is analyzed. We verify that under some constrains on weight function, the Student-r and Student-t distributions maximize the weighted Renyi entropy. Furthermore, an extended version of the Hadamard inequality is derived.