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Theory and practice of the shifted Lotka function

Author

Listed:
  • Leo Egghe

    (Campus Diepenbeek
    Antwerp University (UA), IBW)

  • Ronald Rousseau

    (Antwerp University (UA), IBW
    Faculty of Engineering Technology
    K. U. Leuven)

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.

Suggested Citation

  • Leo Egghe & Ronald Rousseau, 2012. "Theory and practice of the shifted Lotka function," Scientometrics, Springer;Akadémiai Kiadó, vol. 91(1), pages 295-301, April.
    • Handle: RePEc:spr:scient:v:91:y:2012:i:1:d:10.1007_s11192-011-0539-y
    DOI: 10.1007/s11192-011-0539-y
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    References listed on IDEAS

    as
    1. Leo Egghe & Ronald Rousseau, 2006. "An informetric model for the Hirsch-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 121-129, October.
    2. Staša Milojević, 2010. "Power law distributions in information science: Making the case for logarithmic binning," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 61(12), pages 2417-2425, December.
    3. Quentin L. Burrell, 2002. "Will this paper ever be cited?," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 53(3), pages 232-235.
    4. Paul Travis Nicholls, 1987. "Estimation of Zipf parameters," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 38(6), pages 443-445, November.
    5. Leo Egghe & Raf Guns & Ronald Rousseau, 2011. "Thoughts on uncitedness: Nobel laureates and Fields medalists as case studies," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 62(8), pages 1637-1644, August.
    6. Leo Egghe & Raf Guns & Ronald Rousseau, 2011. "Thoughts on uncitedness: Nobel laureates and Fields medalists as case studies," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 62(8), pages 1637-1644, August.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Liu, Joan Q. & Rousseau, Ronald & Wang, Mona S. & Ye, Fred Y., 2013. "Ratios of h-cores, h-tails and uncited sources in sets of scientific papers and technical patents," Journal of Informetrics, Elsevier, vol. 7(1), pages 190-197.
    2. Cena, Anna & Gagolewski, Marek & Siudem, Grzegorz & Żogała-Siudem, Barbara, 2022. "Validating citation models by proxy indices," Journal of Informetrics, Elsevier, vol. 16(2).
    3. Quentin L. Burrell, 2014. "The individual author’s publication–citation process: theory and practice," Scientometrics, Springer;Akadémiai Kiadó, vol. 98(1), pages 725-742, January.

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