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

Tertius de Wet; Ferdinand Österreicher; Maximilian Thaler

doi:10.37920/sasj.2020.54.2.3

Tertius de Wet Department of Statistics and Actuarial Science, University of Stellenbosch, South Africa
Ferdinand Österreicher Department of Mathematics, University of Salzburg, Austria
Maximilian Thaler Department of Mathematics, University of Salzburg, Austria

DOI: https://doi.org/10.37920/sasj.2020.54.2.3

Keywords: Dissimilarity measure (f-divergence), Fisher’s information, Measure of information (entropy)

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.

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