Generalized statistics: yet another generalization

TL;DR

This paper unifies Renyi's and Tsallis's entropies under a common axiomatic framework, revealing their connection to Csiszar's divergence measure used in communication theory.

Contribution

It introduces a new axiomatic system that generalizes and unifies different entropy measures, linking them to established divergence concepts.

Findings

Entropy measures coincide with Csiszar's divergence

Unified framework encompasses Renyi and Tsallis entropies

Provides theoretical foundation for generalized entropy measures

Abstract

We provide a unifying axiomatics for Renyi's entropy and non-extensive entropy of Tsallis. It is shown that the resulting entropy coincides with Csiszar's measure of directed divergence known from communication theory.