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Power laws in citation distributions: evidence from Scopus

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  • Michal Brzezinski

    (University of Warsaw)

Abstract

Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper is concerned with rigorous empirical detection of power-law behaviour in the distribution of citations received by the most highly cited scientific papers. We have used a large, novel data set on citations to scientific papers published between 1998 and 2002 drawn from Scopus. The power-law model is compared with a number of alternative models using a likelihood ratio test. We have found that the power-law hypothesis is rejected for around half of the Scopus fields of science. For these fields of science, the Yule, power-law with exponential cut-off and log-normal distributions seem to fit the data better than the pure power-law model. On the other hand, when the power-law hypothesis is not rejected, it is usually empirically indistinguishable from most of the alternative models. The pure power-law model seems to be the best model only for the most highly cited papers in “Physics and Astronomy”. Overall, our results seem to support theories implying that the most highly cited scientific papers follow the Yule, power-law with exponential cut-off or log-normal distribution. Our findings suggest also that power laws in citation distributions, when present, account only for a very small fraction of the published papers (less than 1 % for most of science fields) and that the power-law scaling parameter (exponent) is substantially higher (from around 3.2 to around 4.7) than found in the older literature.

Suggested Citation

  • Michal Brzezinski, 2015. "Power laws in citation distributions: evidence from Scopus," Scientometrics, Springer;Akadémiai Kiadó, vol. 103(1), pages 213-228, April.
    • Handle: RePEc:spr:scient:v:103:y:2015:i:1:d:10.1007_s11192-014-1524-z
    DOI: 10.1007/s11192-014-1524-z
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    More about this item

    Keywords

    Citation distribution; Power law; Statistical modelling; Scopus;
    All these keywords.

    JEL classification:

    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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