Weighted Approach to General Entropy Function

TL;DR

This paper explores a weighted formulation of general entropy functions, demonstrating that many well-known entropies can be equivalently expressed in this form and applying it to compute Tsallis entropy for mixtures.

Contribution

It establishes the equivalence of weighted and traditional entropy definitions for a broad class of entropy functions, including Shannon, Rényi, and Tsallis.

Findings

Weighted entropy simplifies mixture calculations.

Equivalence shown for Shannon, Rényi, Tsallis entropies.

Application to compute Tsallis entropy of measure mixtures.

Abstract

The definition of weighted entropy allows for easy calculation of the entropy of the mixture of measures. In this paper we investigate the problem of equivalent definition of the general entropy function in weighted form. We show that under reasonable condition, which is satisfied by the well-known Shannon, R\'enyi and Tsallis entropies, every entropy function can be defined equivalently in the weighted way. As a corollary, we show how use the weighted form to compute Tsallis entropy of the mixture of measures.