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The inconsistency of h-index: A mathematical analysis

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  • Brito, Ricardo
  • Navarro, Alonso Rodríguez

Abstract

Citation distributions are lognormal. We use 30 lognormally distributed synthetic series of numbers that simulate real series of citations to investigate the consistency of the h index. Using the lognormal cumulative distribution function, the equation that defines the h index can be formulated; this equation shows that h has a complex dependence on the number of papers (N). We also investigate the correlation between h and the number of papers exceeding various citation thresholds, from 5 to 500 citations. The best correlation is for the 100 threshold but numerous data points deviate from the general trend. The size-independent indicator h/N shows no correlation with the probability of publishing a paper exceeding any of the citation thresholds. In contrast with the h index, the total number of citations shows a high correlation with the number of papers exceeding the thresholds of 10 and 50 citations; the mean number of citations correlates with the probability of publishing a paper that exceeds any level of citations. Thus, in synthetic series, the number of citations and the mean number of citations are much better indicators of research performance than h and h/N. We discuss that in real citation distributions there are other difficulties.

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  • Brito, Ricardo & Navarro, Alonso Rodríguez, 2021. "The inconsistency of h-index: A mathematical analysis," Journal of Informetrics, Elsevier, vol. 15(1).
    • Handle: RePEc:eee:infome:v:15:y:2021:i:1:s1751157720306234
    DOI: 10.1016/j.joi.2020.101106
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    2. Cena, Anna & Gagolewski, Marek & Siudem, Grzegorz & Żogała-Siudem, Barbara, 2022. "Validating citation models by proxy indices," Journal of Informetrics, Elsevier, vol. 16(2).
    3. Katchanov, Yurij L. & Markova, Yulia V. & Shmatko, Natalia A., 2023. "Uncited papers in the structure of scientific communication," Journal of Informetrics, Elsevier, vol. 17(2).
    4. Amodio, Pierluigi & Brugnano, Luigi & Scarselli, Filippo, 2021. "Implementation of the PaperRank and AuthorRank indices in the Scopus database," Journal of Informetrics, Elsevier, vol. 15(4).
    5. Gangan Prathap, 2021. "Letter to the editor: Is the h-index a mock compromise between the p-index and the z-index?," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(5), pages 4537-4539, May.

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