, Volume 91, Issue 1, pp 295-301

First online:

Theory and practice of the shifted Lotka function

  • Leo EggheAffiliated withUniversiteit Hasselt (UHasselt), Campus DiepenbeekAntwerp University (UA), IBW
  • , Ronald RousseauAffiliated withAntwerp University (UA), IBWKHBO (Association K.U.Leuven), Faculty of Engineering TechnologyDepartment of Mathematics, K. U. Leuven Email author 

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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 function Shifted Zipf function Power laws Zero citations