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Are the discretised lognormal and hooked power law distributions plausible for citation data?

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  • Thelwall, Mike

Abstract

There is no agreement over which statistical distribution is most appropriate for modelling citation count data. This is important because if one distribution is accepted then the relative merits of different citation-based indicators, such as percentiles, arithmetic means and geometric means, can be more fully assessed. In response, this article investigates the plausibility of the discretised lognormal and hooked power law distributions for modelling the full range of citation counts, with an offset of 1. The citation counts from 23 Scopus subcategories were fitted to hooked power law and discretised lognormal distributions but both distributions failed a Kolmogorov–Smirnov goodness of fit test in over three quarters of cases. The discretised lognormal distribution also seems to have the wrong shape for citation distributions, with too few zeros and not enough medium values for all subjects. The cause of poor fits could be the impurity of the subject subcategories or the presence of interdisciplinary research. Although it is possible to test for subject subcategory purity indirectly through a goodness of fit test in theory with large enough sample sizes, it is probably not possible in practice. Hence it seems difficult to get conclusive evidence about the theoretically most appropriate statistical distribution.

Suggested Citation

  • Thelwall, Mike, 2016. "Are the discretised lognormal and hooked power law distributions plausible for citation data?," Journal of Informetrics, Elsevier, vol. 10(2), pages 454-470.
  • Handle: RePEc:eee:infome:v:10:y:2016:i:2:p:454-470
    DOI: 10.1016/j.joi.2016.03.001
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    References listed on IDEAS

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    1. Thelwall, Mike, 2016. "The discretised lognormal and hooked power law distributions for complete citation data: Best options for modelling and regression," Journal of Informetrics, Elsevier, vol. 10(2), pages 336-346.
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    11. Thelwall, Mike, 2016. "The precision of the arithmetic mean, geometric mean and percentiles for citation data: An experimental simulation modelling approach," Journal of Informetrics, Elsevier, vol. 10(1), pages 110-123.
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    Citations

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    Cited by:

    1. Mike Thelwall & Kayvan Kousha, 2017. "ResearchGate versus Google Scholar: Which finds more early citations?," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(2), pages 1125-1131, August.
    2. Thelwall, Mike, 2016. "Citation count distributions for large monodisciplinary journals," Journal of Informetrics, Elsevier, vol. 10(3), pages 863-874.
    3. Thelwall, Mike, 2017. "Three practical field normalised alternative indicator formulae for research evaluation," Journal of Informetrics, Elsevier, vol. 11(1), pages 128-151.
    4. Vîiu, Gabriel-Alexandru, 2018. "The lognormal distribution explains the remarkable pattern documented by characteristic scores and scales in scientometrics," Journal of Informetrics, Elsevier, vol. 12(2), pages 401-415.
    5. Confraria, Hugo & Mira Godinho, Manuel & Wang, Lili, 2017. "Determinants of citation impact: A comparative analysis of the Global South versus the Global North," Research Policy, Elsevier, vol. 46(1), pages 265-279.
    6. CholMyong Pak & Guang Yu & Weibin Wang, 2018. "A study on the citation situation within the citing paper: citation distribution of references according to mention frequency," Scientometrics, Springer;Akadémiai Kiadó, vol. 114(3), pages 905-918, March.
    7. Thelwall, Mike, 2016. "Are there too many uncited articles? Zero inflated variants of the discretised lognormal and hooked power law distributions," Journal of Informetrics, Elsevier, vol. 10(2), pages 622-633.
    8. Mike Thelwall, 2019. "The influence of highly cited papers on field normalised indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 118(2), pages 519-537, February.
    9. Guillermo Armando Ronda-Pupo & J. Sylvan Katz, 2017. "The scaling relationship between degree centrality of countries and their citation-based performance on Management Information Systems," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(3), pages 1285-1299, September.
    10. Guillermo Armando Ronda-Pupo & J. Sylvan Katz, 2018. "The power law relationship between citation impact and multi-authorship patterns in articles in Information Science & Library Science journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 114(3), pages 919-932, March.
    11. Thelwall, Mike & Fairclough, Ruth, 2017. "The accuracy of confidence intervals for field normalised indicators," Journal of Informetrics, Elsevier, vol. 11(2), pages 530-540.
    12. Guillermo Armando Ronda-Pupo, 2017. "The citation-based impact of complex innovation systems scales with the size of the system," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(1), pages 141-151, July.

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