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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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    1. Pedro Albarrán & Juan A. Crespo & Ignacio Ortuño & Javier Ruiz-Castillo, 2011. "The skewness of science in 219 sub-fields and a number of aggregates," Scientometrics, Springer;Akadémiai Kiadó, vol. 88(2), pages 385-397, August.
    2. S. Redner, 1998. "How popular is your paper? An empirical study of the citation distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 4(2), pages 131-134, July.
    3. Aristoklis D. Anastasiadis & Marcelo P. Albuquerque & Marcio P. Albuquerque & Diogo B. Mussi, 2010. "Tsallis q-exponential describes the distribution of scientific citations—a new characterization of the impact," Scientometrics, Springer;Akadémiai Kiadó, vol. 83(1), pages 205-218, April.
    4. Pedro Albarrán & Javier Ruiz‐Castillo, 2011. "References made and citations received by scientific articles," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 62(1), pages 40-49, January.
    5. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    6. Michael J Stringer & Marta Sales-Pardo & Luís A Nunes Amaral, 2008. "Effectiveness of Journal Ranking Schemes as a Tool for Locating Information," PLOS ONE, Public Library of Science, vol. 3(2), pages 1-8, February.
    7. Derek De Solla Price, 1976. "A general theory of bibliometric and other cumulative advantage processes," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 27(5), pages 292-306, September.
    8. Aghaei Chadegani, Arezoo & Salehi, Hadi & Md Yunus, Melor & Farhadi, Hadi & Fooladi, Masood & Farhadi, Maryam & Ale Ebrahim, Nader, 2013. "A Comparison between Two Main Academic Literature Collections: Web of Science and Scopus Databases," MPRA Paper 46898, University Library of Munich, Germany, revised 18 Mar 2013.
    9. repec:cte:werepe:we1308 is not listed on IDEAS
    10. Young-Ho Eom & Santo Fortunato, 2011. "Characterizing and Modeling Citation Dynamics," PLOS ONE, Public Library of Science, vol. 6(9), pages 1-7, September.
    11. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    12. Anthony F.J. van Raan, 2006. "Statistical properties of bibliometric indicators: Research group indicator distributions and correlations," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 57(3), pages 408-430, February.
    13. López-Illescas, Carmen & de Moya-Anegón, Félix & Moed, Henk F., 2008. "Coverage and citation impact of oncological journals in the Web of Science and Scopus," Journal of Informetrics, Elsevier, vol. 2(4), pages 304-316.
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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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