Egghe L "The dependence of the height of a Lorenz curve of a Zipf function on the size of the system " Mathematical and Computer Modelling 43(7-8):870-879 April 2006

[Eugene Garfield]

Title: The dependence of the height of a Lorenz curve of a Zipf function on
the size of the system

Author(s): Egghe L

Source: MATHEMATICAL AND COMPUTER MODELLING 43 (7-8): 870-879 APR 2006

Document Type: Article
Language: English
Cited References: 13      Times Cited: 0

Abstract:
The Lorenz curve of a Zipf function describes, graphically, the relation
between the fraction of the items and the fraction of the sources producing
these items. Hence it generalizes the so-called 80/20-rule to general
fractions.
In this paper we examine the relation of such Lorenz curves with the size
of the system (expressed by the total number of sources). We prove that the
height of such a Lorenz curve is an increasing function of the total number
of sources.
In other words, we show that the share of items as a function of the
corresponding share of sources increases with increasing size of the
system. This conclusion is opposite (but not in contradiction) to a
conclusion of Aksnes and Sivertsen (studied in an earlier paper of Egghe)
but where "share of sources" is replaced by "number of sources". (c) 2005
Elsevier Ltd. All rights reserved.

Addresses: Egghe L (reprint author), Univ Hasselt, Diepenbeek, B-3590
Belgium
Univ Hasselt, Diepenbeek, B-3590 Belgium
Univ Antwerp, Antwerp, B-2610 Belgium

E-mail Addresses: leo.egghe at uhasselt.be

Publisher: PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE,
KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Subject Category: COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS;
COMPUTER SCIENCE, SOFTWARE ENGINEERING; MATHEMATICS, APPLIED
IDS Number: 034IE
ISSN: 0895-7177


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