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Dynamic h‐index: The Hirsch index in function of time

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  • Leo Egghe

Abstract

When there are a group of articles and the present time is fixed we can determine the unique number h being the number of articles that received h or more citations while the other articles received a number of citations which is not larger than h. In this article, the time dependence of the h‐index is determined. This is important to describe the expected career evolution of a scientist's work or of a journal's production in a fixed year. We use the earlier established cumulative nth citation distribution. We show that $$ h = ((1 - a^t )^{\alpha - 1} T)^{{1 \over \alpha }} $$ where a is the aging rate, α is the exponent of Lotka's law of the system, and T is the total number of articles in the group. For t = +∞ we refind the steady state (static) formula $h = T^{{1 \over \alpha }}$, which we proved in a previous article. Functional properties of the above formula are proven. Among several results we show (for α, a, T fixed) that h is a concavely increasing function of time, asymptotically bounded by $T^{{1 \over \alpha }}$.

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  • Leo Egghe, 2007. "Dynamic h‐index: The Hirsch index in function of time," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 58(3), pages 452-454, February.
    • Handle: RePEc:bla:jamist:v:58:y:2007:i:3:p:452-454
    DOI: 10.1002/asi.20473
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    Cited by:

    1. Péter Vinkler, 2023. "Impact of the number and rank of coauthors on h-index and π-index. The part-impact method," Scientometrics, Springer;Akadémiai Kiadó, vol. 128(4), pages 2349-2369, April.
    2. Anand Bihari & Sudhakar Tripathi & Akshay Deepak, 2021. "Iterative weighted EM and iterative weighted EM′-index for scientific assessment of scholars," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(7), pages 5551-5568, July.
    3. Péter Vinkler, 2019. "Core journals and elite subsets in scientometrics," Scientometrics, Springer;Akadémiai Kiadó, vol. 121(1), pages 241-259, October.
    4. Kwon, Eunrang & Yun, Jinhyuk & Kang, Jeong-han, 2023. "The effect of the COVID-19 pandemic on gendered research productivity and its correlates," Journal of Informetrics, Elsevier, vol. 17(1).
    5. Chun-Ting Zhang, 2009. "The e-Index, Complementing the h-Index for Excess Citations," PLOS ONE, Public Library of Science, vol. 4(5), pages 1-4, May.

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