, Volume 91, Issue 1, pp 295–301

Theory and practice of the shifted Lotka function


DOI: 10.1007/s11192-011-0539-y

Cite this article as:
Egghe, L. & Rousseau, R. Scientometrics (2012) 91: 295. doi:10.1007/s11192-011-0539-y


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.


Shifted Lotka functionShifted Zipf functionPower lawsZero citations

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  1. 1.Universiteit Hasselt (UHasselt)Campus DiepenbeekDiepenbeekBelgium
  2. 2.Antwerp University (UA), IBWAntwerpenBelgium
  3. 3.KHBO (Association K.U.Leuven)Faculty of Engineering TechnologyOostendeBelgium
  4. 4.Department of MathematicsK. U. LeuvenLeuven (Heverlee)Belgium