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Theory and practice of the shifted Lotka function

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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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Authors and Affiliations

  1. Universiteit Hasselt (UHasselt), Campus Diepenbeek, Agoralaan, 3590, Diepenbeek, Belgium

    Leo Egghe

  2. Antwerp University (UA), IBW, Venusstraat 35, 2000, Antwerpen, Belgium

    Leo Egghe & Ronald Rousseau

  3. KHBO (Association K.U.Leuven), Faculty of Engineering Technology, Zeedijk 101, 8400, Oostende, Belgium

    Ronald Rousseau

  4. Department of Mathematics, K. U. Leuven, Celestijnenlaan 200B, 3000, Leuven (Heverlee), Belgium

    Ronald Rousseau

Authors
  1. Leo Egghe
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  2. Ronald Rousseau
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Correspondence to Ronald Rousseau.

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Egghe, L., Rousseau, R. Theory and practice of the shifted Lotka function. Scientometrics 91, 295–301 (2012). https://doi.org/10.1007/s11192-011-0539-y

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  • DOI: https://doi.org/10.1007/s11192-011-0539-y

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