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The mathematical relation between the impact factor and the uncitedness factor

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  • Leo Egghe

    (Universiteit Hasselt (UHasselt)
    Universiteit Antwerpen (UA))

Abstract

In a general framework, given a set of articles and their received citations (time periods of publication or citation are not important here) one can define the impact factor (IF) as the total number of received citations divided by the total number of publications (articles). The uncitedness factor (UF) is defined as the fraction of the articles that received no citations. It is intuitively clear that IF should be a decreasing function of UF. This is confirmed by the results in [van Leeuwen & Moed, 2005] but all the given examples show a typical shape, seldom seen in informetrics: a horizontal S-shape (first convex then concave). Adopting a simple model for the publication-citation relation, we prove this horizontal S-shape in this paper, showing that such a general functional relationship can be generally explained.

Suggested Citation

  • Leo Egghe, 2008. "The mathematical relation between the impact factor and the uncitedness factor," Scientometrics, Springer;Akadémiai Kiadó, vol. 76(1), pages 117-123, July.
    • Handle: RePEc:spr:scient:v:76:y:2008:i:1:d:10.1007_s11192-007-1902-x
    DOI: 10.1007/s11192-007-1902-x
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    References listed on IDEAS

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    1. Thed N. van Leeuwen & Henk F. Moed, 2005. "Characteristics of journal impact factors: The effects of uncitedness and citation distribution on the understanding of journal impact factors," Scientometrics, Springer;Akadémiai Kiadó, vol. 63(2), pages 357-371, April.
    2. Tove Faber Frandsen & Ronald Rousseau, 2005. "Article impact calculated over arbitrary periods," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 56(1), pages 58-62, January.
    3. Burrell, Quentin L., 2007. "Hirsch's h-index: A stochastic model," Journal of Informetrics, Elsevier, vol. 1(1), pages 16-25.
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    Cited by:

    1. L. Egghe, 2010. "The distribution of the uncitedness factor and its functional relation with the impact factor," Scientometrics, Springer;Akadémiai Kiadó, vol. 83(3), pages 689-695, June.
    2. Wolfgang Glänzel, 2009. "The multi-dimensionality of journal impact," Scientometrics, Springer;Akadémiai Kiadó, vol. 78(2), pages 355-374, February.
    3. Hu, Zewen & Wu, Yishan, 2014. "Regularity in the time-dependent distribution of the percentage of never-cited papers: An empirical pilot study based on the six journals," Journal of Informetrics, Elsevier, vol. 8(1), pages 136-146.
    4. Zewen Hu & Yishan Wu & Jianjun Sun, 2018. "A quantitative analysis of determinants of non-citation using a panel data model," Scientometrics, Springer;Akadémiai Kiadó, vol. 116(2), pages 843-861, August.
    5. Egghe, L., 2009. "Mathematical derivation of the impact factor distribution," Journal of Informetrics, Elsevier, vol. 3(4), pages 290-295.
    6. Egghe, L., 2013. "The functional relation between the impact factor and the uncitedness factor revisited," Journal of Informetrics, Elsevier, vol. 7(1), pages 183-189.
    7. Burrell, Quentin L., 2013. "A stochastic approach to the relation between the impact factor and the uncitedness factor," Journal of Informetrics, Elsevier, vol. 7(3), pages 676-682.

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