Tsallis’ entropies — Axiomatics, associated f-divergences and Fisher’s information

Abstract

In a previous paper, de Wet and Österreicher (2016) showed how Arimoto’s extended class of entropies generates a family of f-divergences leading to approximation results and finally to Fisher’s information in a limiting way. In the current paper, the so-called Tsallis class of entropies is used in a similar fashion to generate a new family of f-divergences with analogous properties. The approximation properties are proved in a form which significantly generalizes the corresponding results in the above mentioned paper.