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Zipf’s law and log-normal distributions in measures of scientific output across fields and institutions: 40 years of Slovenia’s research as an example


  • Perc, Matjaž


Slovenia’s Current Research Information System (SICRIS) currently hosts 86,443 publications with citation data from 8359 researchers working on the whole plethora of social and natural sciences from 1970 till present. Using these data, we show that the citation distributions derived from individual publications have Zipfian properties in that they can be fitted by a power law P(x)∼x−α, with α between 2.4 and 3.1 depending on the institution and field of research. Distributions of indexes that quantify the success of researchers rather than individual publications, on the other hand, cannot be associated with a power law. We find that for Egghe’s g-index and Hirsch’s h-index the log-normal form P(x)∼exp⁡[−aln⁡x−b(ln⁡x)2] applies best, with a and b depending moderately on the underlying set of researchers. In special cases, particularly for institutions with a strongly hierarchical constitution and research fields with high self-citation rates, exponential distributions can be observed as well. Both indexes yield distributions with equivalent statistical properties, which is a strong indicator for their consistency and logical connectedness. At the same time, differences in the assessment of citation histories of individual researchers strengthen their importance for properly evaluating the quality and impact of scientific output.

Suggested Citation

  • Perc, Matjaž, 2010. "Zipf’s law and log-normal distributions in measures of scientific output across fields and institutions: 40 years of Slovenia’s research as an example," Journal of Informetrics, Elsevier, vol. 4(3), pages 358-364.
  • Handle: RePEc:eee:infome:v:4:y:2010:i:3:p:358-364
    DOI: 10.1016/j.joi.2010.03.001

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    References listed on IDEAS

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    6. Egghe, L., 2009. "Mathematical derivation of the impact factor distribution," Journal of Informetrics, Elsevier, vol. 3(4), pages 290-295.
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    Cited by:

    1. repec:spr:scient:v:112:y:2017:i:1:d:10.1007_s11192-017-2359-1 is not listed on IDEAS
    2. repec:eee:infome:v:12:y:2018:i:2:p:401-415 is not listed on IDEAS
    3. Andrej Kastrin & Jelena Klisara & Borut Lužar & Janez Povh, 2017. "Analysis of Slovenian research community through bibliographic networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 110(2), pages 791-813, February.
    4. Perc, Matjaž, 2010. "Growth and structure of Slovenia’s scientific collaboration network," Journal of Informetrics, Elsevier, vol. 4(4), pages 475-482.
    5. repec:spr:scient:v:102:y:2015:i:1:d:10.1007_s11192-014-1398-0 is not listed on IDEAS
    6. Sangwal, Keshra, 2013. "Comparison of different mathematical functions for the analysis of citation distribution of papers of individual authors," Journal of Informetrics, Elsevier, vol. 7(1), pages 36-49.
    7. Tol, Richard S.J., 2013. "The Matthew effect for cohorts of economists," Journal of Informetrics, Elsevier, vol. 7(2), pages 522-527.
    8. Mario Karlovčec & Borut Lužar & Dunja Mladenić, 2016. "Core-periphery dynamics in collaboration networks: the case study of Slovenia," Scientometrics, Springer;Akadémiai Kiadó, vol. 109(3), pages 1561-1578, December.
    9. Bertoli-Barsotti, Lucio & Lando, Tommaso, 2015. "On a formula for the h-index," Journal of Informetrics, Elsevier, vol. 9(4), pages 762-776.
    10. Vieira, Elizabeth S. & Lepori, Benedetto, 2016. "The growth process of higher education institutions and public policies," Journal of Informetrics, Elsevier, vol. 10(1), pages 286-298.
    11. Sangwal, Keshra, 2014. "Distributions of citations of papers of individual authors publishing in different scientific disciplines: Application of Langmuir-type function," Journal of Informetrics, Elsevier, vol. 8(4), pages 972-984.
    12. Lina M. Cortés & Andrés Mora-Valencia & Javier Perote, 2016. "The productivity of top researchers: a semi-nonparametric approach," Scientometrics, Springer;Akadémiai Kiadó, vol. 109(2), pages 891-915, November.


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