MONOTONICITY OF THE JENSEN FUNCTIONAL FOR f- DIVERGENCES WITH APPLICATIONS TO THE ZIPF-MANDELBROT LAW

The Jensen functional in its discrete form is brought in relation to the Csiszar divergence functional via its monotonicity property. Thus deduced general results branch into specific forms for some of the well known f- divergences, e.g. the Kullback-Leibler divergence, the Hellinger distance, the Bhattacharyya coefficient, chi(2)- divergence, total variation distance. Obtained comparative inequalities are also interpreted in the environment of the Zipf and the Zipf-Mandelbrot law.

Authors
Lovricevic N.1 , Pecaric D.2 , Pecaric J. 3
Publisher
Element D.O.O.
Number of issue
4
Language
English
Pages
1427-1449
Status
Published
Volume
22
Year
2019
Organizations
  • 1 Univ Split, Fac Civil Engn Architecture & Geodesy, Matice Hrvatske 15, Split 21000, Croatia
  • 2 Catholic Univ Croatia, Ilica 242, Zagreb 10000, Croatia
  • 3 RUDN Univ, Miklukho Maklaya Str 6, Moscow 117198, Russia
Keywords
Monotonicity property; Jensen's functional; Zipf 's and Zipf-Mandelbrot's law; Csiszar divergence functional; f - divergences
Date of creation
24.12.2019
Date of change
24.12.2019
Short link
https://repository.rudn.ru/en/records/article/record/55647/