Weighted Approach to General Entropy Function

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.