Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

psi-Hilfer Fractional Approximations of Csiszar's f-Divergence

Version 1 : Received: 3 March 2021 / Approved: 4 March 2021 / Online: 4 March 2021 (14:19:06 CET)

How to cite: Anastassiou, G. psi-Hilfer Fractional Approximations of Csiszar's f-Divergence. Preprints 2021, 2021030166 (doi: 10.20944/preprints202103.0166.v1). Anastassiou, G. psi-Hilfer Fractional Approximations of Csiszar's f-Divergence. Preprints 2021, 2021030166 (doi: 10.20944/preprints202103.0166.v1).

Abstract

Here are given tight probabilistic inequalities that provide nearly best estimates for the Csiszar's f-divergence. These use the right and left psi -Hilfer fractional derivatives of the directing function f. Csiszar's f- divergence or the so called Csiszar's discrimination is used as a measure of dependence between two random variables which is a very essential aspect of stochastics, we apply our results there. The Csiszar's discrimination is the most important and general measure for the comparison between two probability measures. We give also other applications.

Keywords

Csiszar's discrimination; Csiszar's distance; fractional calculus; psi-Hilfer fractional derivative

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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