Hybrid Zipf-Mandelbrot law

There is a unified approach, maximization of Shannon entropy, that naturally follows the path of generalization from Zipf's to hybrid Zipf's law. Extending this idea we make transition from Zipf-Mandelbrot to hybrid Zipf-Mandelbrot law. It is interesting that examination of its densities provides some new insights of Lerch's transcendent. © ELEMENT, Zagreb.

Авторы
Jakšetić J. 1 , Pečarić D. 2 , Pečarić J. 3, 4
Journal
Journal of Mathematical Inequalities
Издательство
Element D.O.O.
Номер выпуска
1
Язык
English
Страницы
275-286
Статус
Published
Ссылка
Внешняя ссылка
DOI
10.7153/JMI-2019-13-20
Том
13
Год
2019
Организации
  • 1 Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, Zagreb, 10000, Croatia
  • 2 Catholic University of Croatia, Ilica 242, Zagreb, 10000, Croatia
  • 3 Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia
  • 4 RUDN University, Miklukho-Maklaya str.6, Moscow, 117198, Russian Federation
Ключевые слова
Chebyshev's inequality; Lerch's transcendent; Log-convex functions; Lyapunov's inequality; Shannon entropy; Zipf-Mandelbrot law
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