Majorizatiuon and Zipf-Mandelbrot law

In this paper we show how the Zipf-Mandelbrot law is connected to the theory of majorization. Firstly we consider the Csiszar f-divergence for the Zipf-Mandelbrot law and then develop important majorization inequalities for these divergences. We also discuss some special cases for our generalized results by using the Zipf-Mandelbrot law. As applications, we present the majorization inequalities for various distances obtaining by some special convex functions in the Csiszar f-divergence for Z-M law like the Renyi alpha-order entropy for Z-M law, variational distance for Z-M law, the Hellinger distance for Z-M law, chi(2)-distance for Z-M law and triangular discrimination for Z-M law. At the end, we give important applications of the Zipf's law in linguistics and obtain the bounds for the Kullback-Leibler divergence of the distributions associated to the English and the Russian languages.

Авторы
Latif N.1 , Pecaric D.2 , Pecaric J. 3, 4
Издательство
TBILISI CENTRE MATH SCI
Номер выпуска
3
Язык
Английский
Страницы
1-27
Статус
Опубликовано
Том
11
Год
2018
Организации
  • 1 Jubail Ind Coll, Dept Gen Studies, Jubail Ind City 31961, Saudi Arabia
  • 2 Catholic Univ Croatia, Ilica 242, Zagreb 10000, Croatia
  • 3 Univ Zagreb, Fac Text Technol Zagreb, Prilaz Baruna Filipovica 28A, Zagreb 10000, Croatia
  • 4 RUDN Univ, 6 Miklukho Maklay St, Moscow 117198, Russia
Ключевые слова
Majorization inequailty; Csiszar f-divergence; Zipf-Mandelbrot law; Zipf's law in linguistic; Renyi alpha-order entropy; variational distance; Hellinger discrimination; chi(2)-distance and triangular discrimination
Дата создания
19.05.2021
Дата изменения
19.05.2021
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/73440/
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