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The Hirsch index of a shifted Lotka function and its relation with the impact factor

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  • Leo Egghe
  • Ronald Rousseau

Abstract

Based on earlier results about the shifted Lotka function, we prove an implicit functional relation between the Hirsch index (h‐index) and the total number of sources (T). It is shown that the corresponding function, h(T), is concavely increasing. Next, we construct an implicit relation between the h‐index and the impact factor IF (an average number of items per source). The corresponding function h(IF) is increasing and we show that if the parameter C in the numerator of the shifted Lotka function is high, then the relation between the h‐index and the impact factor is almost linear.

Suggested Citation

  • Leo Egghe & Ronald Rousseau, 2012. "The Hirsch index of a shifted Lotka function and its relation with the impact factor," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 63(5), pages 1048-1053, May.
    • Handle: RePEc:bla:jamist:v:63:y:2012:i:5:p:1048-1053
    DOI: 10.1002/asi.22617
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    Cited by:

    1. Bertoli-Barsotti, Lucio & Lando, Tommaso, 2019. "How mean rank and mean size may determine the generalised Lorenz curve: With application to citation analysis," Journal of Informetrics, Elsevier, vol. 13(1), pages 387-396.
    2. Liu, Joan Q. & Rousseau, Ronald & Wang, Mona S. & Ye, Fred Y., 2013. "Ratios of h-cores, h-tails and uncited sources in sets of scientific papers and technical patents," Journal of Informetrics, Elsevier, vol. 7(1), pages 190-197.
    3. 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.
    4. 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.
    5. Egghe, L., 2014. "Impact coverage of the success-index," Journal of Informetrics, Elsevier, vol. 8(2), pages 384-389.
    6. Bertoli-Barsotti, Lucio & Lando, Tommaso, 2015. "On a formula for the h-index," Journal of Informetrics, Elsevier, vol. 9(4), pages 762-776.
    7. Burrell, Quentin L., 2013. "The h-index: A case of the tail wagging the dog?," Journal of Informetrics, Elsevier, vol. 7(4), pages 774-783.
    8. M. Ausloos, 2013. "A scientometrics law about co-authors and their ranking: the co-author core," Scientometrics, Springer;Akadémiai Kiadó, vol. 95(3), pages 895-909, June.
    9. Lucio Bertoli-Barsotti & Tommaso Lando, 2017. "A theoretical model of the relationship between the h-index and other simple citation indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 111(3), pages 1415-1448, June.

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