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  • 1 Universiteit Hasselt (UHasselt), Campus Diepenbeek, Agoralaan, 3590 Diepenbeek, Belgium leo.egghe@uhasselt.be
  • 2 Antwerp University (UA), IBW, Venusstraat 35, 2000 Antwerpen, Belgium
  • 3 KHBO (Association K. U. Leuven), Faculty of Engineering Technology, Zeedijk 101, 8400 Oostende, Belgium
  • 4 Department of Mathematics, K. U. Leuven, Celestijnenlaan 200B, 3000 Leuven (Heverlee), Belgium
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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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