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How mean rank and mean size may determine the generalised Lorenz curve: With application to citation analysis

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  • Bertoli-Barsotti, Lucio
  • Lando, Tommaso

Abstract

Within the wide framework of information production processes, we present a conversion formula that expresses the generalised Lorenz (GL) curve of a size-frequency distribution as a function of the corresponding rank-size distribution using a fully discrete modelling approach. Based on this conversion formula, we introduce a somewhat universal model for the GL curve of the empirical size-frequency distribution. This study’s approach to determining the GL curve is indirect, as we obtain our model for the size-frequency framework by modelling the rank-size distribution and not by directly modelling the size distribution or the GL curve itself, as is usually done. Our GL curve model is particularly appealing because it provides a simple and economical description of the distribution that depends on only three quantities: the (i) mean size, (ii) mean rank, and (iii) maximal rank. The model’s performance in predicting the shape of the empirical GL curve is illustrated through a case study involving citation analysis.

Suggested Citation

  • Bertoli-Barsotti, Lucio & Lando, Tommaso, 2019. "How mean rank and mean size may determine the generalised Lorenz curve: With application to citation analysis," Journal of Informetrics, Elsevier, vol. 13(1), pages 387-396.
    • Handle: RePEc:eee:infome:v:13:y:2019:i:1:p:387-396
    DOI: 10.1016/j.joi.2019.02.003
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    References listed on IDEAS

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    Cited by:

    1. Lucio Bertoli-Barsotti, 2023. "Equivalent Gini coefficient, not shape parameter!," Scientometrics, Springer;Akadémiai Kiadó, vol. 128(1), pages 867-870, January.
    2. Lucio Bertoli-Barsotti & Marek Gagolewski & Grzegorz Siudem & Barbara .Zoga{l}a-Siudem, 2023. "Equivalence of inequality indices: Three dimensions of impact revisited," Papers 2304.07479, arXiv.org.
    3. Aktaev, Nurken E. & Bannova, K.A., 2022. "Mathematical modeling of probability distribution of money by means of potential formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    4. Lucio Bertoli-Barsotti & Marek Gagolewski & Grzegorz Siudem & Barbara .Zoga{l}a-Siudem, 2023. "Gini-stable Lorenz curves and their relation to the generalised Pareto distribution," Papers 2304.07480, arXiv.org, revised Jan 2024.
    5. Biró, Tamás S. & Telcs, András & Józsa, Máté & Néda, Zoltán, 2023. "Gintropic scaling of scientometric indexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    6. Mrowinski, Maciej J. & Gagolewski, Marek & Siudem, Grzegorz, 2022. "Accidentality in journal citation patterns," Journal of Informetrics, Elsevier, vol. 16(4).
    7. Thitithep Sitthiyot & Kanyarat Holasut, 2020. "A simple method for measuring inequality," Palgrave Communications, Palgrave Macmillan, vol. 6(1), pages 1-9, December.

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