Scientometrics
Volume/Issue:
Volume 91: Issue 1
Theory and practice of the shifted Lotka function
Authors:
Leo Egghe Universiteit Hasselt (UHasselt), Campus Diepenbeek, Agoralaan, 3590 Diepenbeek, Belgium leo.egghe@uhasselt.be
Antwerp University (UA), IBW, Venusstraat 35, 2000 Antwerpen, Belgium

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and
Ronald Rousseau Antwerp University (UA), IBW, Venusstraat 35, 2000 Antwerpen, Belgium
KHBO (Association K. U. Leuven), Faculty of Engineering Technology, Zeedijk 101, 8400 Oostende, Belgium
Department of Mathematics, K. U. Leuven, Celestijnenlaan 200B, 3000 Leuven (Heverlee), Belgium

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Pages:
295–301
Online Publication Date:
15 Oct 2011
Publication Date:
01 Apr 2012
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s11192-011-0539-y
Keywords:
Shifted Lotka function; Shifted Zipf function; Power laws; Zero citations
Restricted access

Abstract

One of the major drawbacks of the classical Lotka function is that arguments only start from the value 1. However, in many applications one may want to start from the value 0, e.g. when including zero received citations. In this article we consider the shifted Lotka function, which includes the case of zero items. Basic results for the total number of sources, the total number of items and the average number of items per source are given in this framework. Next we give the rank-frequency function (Zipf-type function) corresponding to the shifted Lotka function and prove their exact relation. The article ends with a practical example which can be fitted by a shifted Lotka function.

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Cover Scientometrics
Scientometrics
Print ISSN:
0138-9130
Online ISSN:
1588-2861

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Scientometrics
Language English
Size B5
Year of
Foundation		 1978
Volumes
per Year		 1
Issues
per Year		 12
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0138-9130 (Print)
ISSN 1588-2861 (Online)

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