Some properties of zipf–mandelbrot law and hurwitz ? –function

In this paper we deal with analytical properties of the Zipf-Mandelbrot law. If total mass of this law is spread all over positive integers we come to Hurwitz ? -function. As we show, it is very natural first to examine properties of Hurwitz ? -function to derive properties of Zipf-Mandelbrot law. Using some well-known inequalities such as Chebyshev’s and Lyapunov’s inequality we are able to deduce a whole variety of theoretical characterizations that include, among others, log-convexity, log-subadditivity, exponential convexity.

Авторы
Jakšeti J.1 , Peari D.2 , Peari J. 3, 4
Издательство
Element D.O.O.
Номер выпуска
2
Язык
Английский
Страницы
575-584
Статус
Опубликовано
Том
21
Год
2018
Организации
  • 1 Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lu?i?a 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; Hurwitz ? -function; Log-convexity; Lyapunov’s inequality; Zipf-Mandelbrot law
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6755/