SOME PROPERTIES OF ZIPF-MANDELBROT LAW AND HURWITZ ζ-FUNCTION

被引：20

作者：

Jaksetic, Julije ^{[1
]}

Pecaric, Dilda ^{[2
]}

Pecaric, Josip ^{[3
,4
]}

机构：

[1] Univ Zagreb, Fac Mech Engn & Naval Architecture, Ivana Lucica 5, Zagreb 10000, Croatia

[2] Catholic Univ Croatia, Ilica 242, Zagreb 10000, Croatia

[3] Univ Zagreb, Fac Text Technol, Zagreb, Croatia

[4] RUDN Univ, Miklukho Maklaya Str 6, Moscow 117198, Russia

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2018年 / 21卷 / 02期

关键词：

Zipf-Mandelbrot law; Hurwitz zeta-function; log-convexity; Chebyshev's inequality; Lyapunov's inequality; DIVERSITY;

D O I：

10.7153/mia-2018-21-42

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 lambda-function. As we show, it is very natural first to examine properties of Hurwitz zeta-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.

引用

页码：575 / 584

页数：10

共 12 条

[1]

[Anonymous], 1949, Human behaviour and the principle of least-effort

[2] Convesity, complete monotonicity and inequalities on zeta and gamma functions, on functions of Baskov operators and on arithmetic functions [J].

Bastien, G ;

Rogalski, M .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2002, 54 (05) :916-944

[3]

FRONTIER S, 1985, OCEANOGR MAR BIOL, V23, P253

[4]

HORVATH L., B MALAYS MA IN PRESS

[5]

Jaksetic J, 2013, J CONVEX ANAL, V20, P181

[6]

Lelu A., 2014, Boletin de Estadistica e Investigacion Operativa, V30, P66

[7]

MANDELBROT B, 1953, COMMUNICATION THEORY

[8] Mandelbrot's Model for Zipf's Law Can Mandelbrot's Model Explain Zipf's Law for Language? [J].

Manin, D. Yu. .

JOURNAL OF QUANTITATIVE LINGUISTICS, 2009, 16 (03) :274-285

[9] Introduction of relative abundance distribution (RAD) indices, estimated from the rank-frequency diagrams (RFD), to assess changes in community diversity [J].

Mouillot, D ;

Lepretre, A .

ENVIRONMENTAL MONITORING AND ASSESSMENT, 2000, 63 (02) :279-295

[10]

PECARIC J., 1996, NEJEDNAKOSTI

← 1 2 →