Some New $f$-Divergence Measures and Their Basic Properties

Sever Dragomır

doi:10.36753/mathenot.1362706

EN

Some New $f$-Divergence Measures and Their Basic Properties

Abstract

In this paper, we introduce some new $f$-divergence measures that we call $t$-\textit{asymmetric/symmetric divergence measure} and\textit{\ integral divergence measure, }establish their joint convexity and provide some inequalities that connect these $f$-divergences to the classical one introduced by Csiszar in 1963. Applications for the \textit{dichotomy class} of convex functions are provided as well.

Keywords

$f$-divergence measures, Hellinger discrimination, HH $f$-divergence measures, Jeffrey, Kullback-Leibler divergence, $\chi ^{2}$-divergence

References

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Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods, Applied Mathematics (Other)

Journal Section

Research Article

Authors

Sever Dragomır ^*
0000-0003-2902-6805
Australia

Early Pub Date

January 21, 2024

Publication Date

April 14, 2024

Submission Date

September 19, 2023

Acceptance Date

January 4, 2024

Published in Issue

Year 2024 Volume: 12 Number: 2

DOI

https://doi.org/10.36753/mathenot.1362706

IZ

https://izlik.org/JA92ZW34YE

APA

Dragomır, S. (2024). Some New $f$-Divergence Measures and Their Basic Properties. Mathematical Sciences and Applications E-Notes, 12(2), 43-59. https://doi.org/10.36753/mathenot.1362706

AMA

1.Dragomır S. Some New $f$-Divergence Measures and Their Basic Properties. Math. Sci. Appl. E-Notes. 2024;12(2):43-59. doi:10.36753/mathenot.1362706

Chicago

Dragomır, Sever. 2024. “Some New $f$-Divergence Measures and Their Basic Properties”. Mathematical Sciences and Applications E-Notes 12 (2): 43-59. https://doi.org/10.36753/mathenot.1362706.

EndNote

Dragomır S (April 1, 2024) Some New $f$-Divergence Measures and Their Basic Properties. Mathematical Sciences and Applications E-Notes 12 2 43–59.

IEEE

[1]S. Dragomır, “Some New $f$-Divergence Measures and Their Basic Properties”, Math. Sci. Appl. E-Notes, vol. 12, no. 2, pp. 43–59, Apr. 2024, doi: 10.36753/mathenot.1362706.

ISNAD

Dragomır, Sever. “Some New $f$-Divergence Measures and Their Basic Properties”. Mathematical Sciences and Applications E-Notes 12/2 (April 1, 2024): 43-59. https://doi.org/10.36753/mathenot.1362706.

JAMA

1.Dragomır S. Some New $f$-Divergence Measures and Their Basic Properties. Math. Sci. Appl. E-Notes. 2024;12:43–59.

MLA

Dragomır, Sever. “Some New $f$-Divergence Measures and Their Basic Properties”. Mathematical Sciences and Applications E-Notes, vol. 12, no. 2, Apr. 2024, pp. 43-59, doi:10.36753/mathenot.1362706.

Vancouver

1.Sever Dragomır. Some New $f$-Divergence Measures and Their Basic Properties. Math. Sci. Appl. E-Notes. 2024 Apr. 1;12(2):43-59. doi:10.36753/mathenot.1362706