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

George Anastassiou

doi:10.20944/preprints202103.0166.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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.

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

Computer Science and Mathematics, Algebra and Number Theory

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

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