Zipf–Mandelbrot law, f-divergences and the Jensen-type interpolating inequalities

Motivated by the method of interpolating inequalities that makes use of the improved Jensen-type inequalities, in this paper we integrate this approach with the well known Zipf–Mandelbrot law applied to various types of f-divergences and distances, such are Kullback–Leibler divergence, Hellinger distance, Bhattacharyya distance (via coefficient), χ2-divergence, total variation distance and triangular discrimination. Addressing these applications, we firstly deduce general results of the type for the Csiszár divergence functional from which the listed divergences originate. When presenting the analyzed inequalities for the Zipf–Mandelbrot law, we accentuate its special form, the Zipf law with its specific role in linguistics. We introduce this aspect through the Zipfian word distribution associated to the English and Russian languages, using the obtained bounds for the Kullback–Leibler divergence. © 2018, The Author(s).

Авторы
Lovričević N.1 , Pečarić Ð.2 , Pečarić J. 3, 4
Редакторы
-
Издательство
Springer International Publishing
Номер выпуска
-
Язык
Английский
Страницы
-
Статус
Опубликовано
Подразделение
-
Номер
36
Том
2018
Год
2018
Организации
  • 1 Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Split, Croatia
  • 2 Catholic University of Croatia, Zagreb, Croatia
  • 3 Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia
  • 4 RUDN University, Moscow, Russian Federation
Ключевые слова
Csiszár divergence functional; f-divergences; Jensen inequality; Kullback–Leibler divergence; Zipf and Zipf–Mandelbrot law
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/7321/