IDEAS home Printed from https://ideas.repec.org/a/eee/infome/v13y2019i1p291-298.html
   My bibliography  Save this article

Infinite sequences and their h-type indices

Author

Listed:
  • Egghe, Leo
  • Rousseau, Ronald

Abstract

Starting from the notion of h-type indices for infinite sequences we investigate if these indices satisfy natural inequalities related to the arithmetic, the geometric and the harmonic mean. If f denotes an h-type index, such as the h- or the g-index, then we investigate inequalities such as min(f(X),f(Y)) ≤ f((X + Y)/2) ≤ max(f(X), f(Y)). We further investigate if: f(min(X,Y)) = min(f(X),f(Y)) and if f(max(X,Y)) = max(f(X),f(Y)). It is shown that the h-index satisfies all the equalities and inequalities we investigate but the g-index does not always, while it is always possible to find a counterexample involving the R-index. This shows that the h-index enjoys a number of interesting mathematical properties as an operator in the partially ordered positive cone (R+)∞ of all infinite sequences with non-negative real values.

Suggested Citation

  • Egghe, Leo & Rousseau, Ronald, 2019. "Infinite sequences and their h-type indices," Journal of Informetrics, Elsevier, vol. 13(1), pages 291-298.
    • Handle: RePEc:eee:infome:v:13:y:2019:i:1:p:291-298
    DOI: 10.1016/j.joi.2019.01.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1751157718304486
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.joi.2019.01.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Leo Egghe, 2006. "Theory and practise of the g-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 131-152, October.
    2. Denis Bouyssou & Thierry Marchant, 2011. "Ranking scientists and departments in a consistent manner," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 62(9), pages 1761-1769, September.
    3. Vladimir G. Deineko & Gerhard J. Woeginger, 2009. "A new family of scientific impact measures: The generalized Kosmulski-indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 80(3), pages 819-826, September.
    4. Ludo Waltman & Nees Jan van Eck, 2012. "The inconsistency of the h-index," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 63(2), pages 406-415, February.
    5. Ronald Rousseau, 2016. "Citation data as a proxy for quality or scientific influence are at best PAC (probably approximately correct)," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 67(12), pages 3092-3094, December.
    6. Egghe, L., 2011. "Characterizations of the generalized Wu- and Kosmulski-indices in Lotkaian systems," Journal of Informetrics, Elsevier, vol. 5(3), pages 439-445.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Leo Egghe & Ronald Rousseau, 2021. "The h-index formalism," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(7), pages 6137-6145, July.
    2. Leo Egghe & Ronald Rousseau, 2020. "Minimal Impact One-Dimensional Arrays," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    3. Egghe, Leo & Rousseau, Ronald, 2020. "Polar coordinates and generalized h-type indices," Journal of Informetrics, Elsevier, vol. 14(2).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Leo Egghe & Ronald Rousseau, 2019. "Measures of linear type lead to a characterization of Zipf functions," Scientometrics, Springer;Akadémiai Kiadó, vol. 121(3), pages 1707-1715, December.
    2. Bouyssou, Denis & Marchant, Thierry, 2014. "An axiomatic approach to bibliometric rankings and indices," Journal of Informetrics, Elsevier, vol. 8(3), pages 449-477.
    3. Yves Fassin, 2020. "The HF-rating as a universal complement to the h-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 125(2), pages 965-990, November.
    4. Leo Egghe & Ronald Rousseau, 2020. "Minimal Impact One-Dimensional Arrays," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    5. Brandão, Luana Carneiro & Soares de Mello, João Carlos Correia Baptista, 2019. "A multi-criteria approach to the h-index," European Journal of Operational Research, Elsevier, vol. 276(1), pages 357-363.
    6. Ana Paula dos Santos Rubem & Ariane Lima Moura & João Carlos Correia Baptista Soares de Mello, 2015. "Comparative analysis of some individual bibliometric indices when applied to groups of researchers," Scientometrics, Springer;Akadémiai Kiadó, vol. 102(1), pages 1019-1035, January.
    7. Leo Egghe & Ronald Rousseau, 2021. "The h-index formalism," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(7), pages 6137-6145, July.
    8. Giovanni Abramo & Ciriaco Andrea D’Angelo & Fulvio Viel, 2013. "The suitability of h and g indexes for measuring the research performance of institutions," Scientometrics, Springer;Akadémiai Kiadó, vol. 97(3), pages 555-570, December.
    9. Bouyssou, Denis & Marchant, Thierry, 2016. "Ranking authors using fractional counting of citations: An axiomatic approach," Journal of Informetrics, Elsevier, vol. 10(1), pages 183-199.
    10. Egghe, L., 2014. "Impact coverage of the success-index," Journal of Informetrics, Elsevier, vol. 8(2), pages 384-389.
    11. Lutz Bornmann & Werner Marx, 2014. "How to evaluate individual researchers working in the natural and life sciences meaningfully? A proposal of methods based on percentiles of citations," Scientometrics, Springer;Akadémiai Kiadó, vol. 98(1), pages 487-509, January.
    12. Josep Freixas & Roger Hoerl & William S. Zwicker, 2023. "Nash's bargaining problem and the scale-invariant Hirsch citation index," Papers 2309.01192, arXiv.org.
    13. Chambers, Christopher P. & Miller, Alan D., 2014. "Scholarly influence," Journal of Economic Theory, Elsevier, vol. 151(C), pages 571-583.
    14. Waltman, Ludo, 2016. "A review of the literature on citation impact indicators," Journal of Informetrics, Elsevier, vol. 10(2), pages 365-391.
    15. Egghe, L., 2013. "A mathematical characterization of the Hirsch-index by means of minimal increments," Journal of Informetrics, Elsevier, vol. 7(2), pages 388-393.
    16. Fassin, Yves, 2024. "The internal dynamics of journals’ h-cores over time," Journal of Informetrics, Elsevier, vol. 18(2).
    17. Jianhua Hou & Xiucai Yang & Chaomei Chen, 2018. "Emerging trends and new developments in information science: a document co-citation analysis (2009–2016)," Scientometrics, Springer;Akadémiai Kiadó, vol. 115(2), pages 869-892, May.
    18. Lutz Bornmann & Loet Leydesdorff, 2018. "Count highly-cited papers instead of papers with h citations: use normalized citation counts and compare “like with like”!," Scientometrics, Springer;Akadémiai Kiadó, vol. 115(2), pages 1119-1123, May.
    19. Loet Leydesdorff & Paul Wouters & Lutz Bornmann, 2016. "Professional and citizen bibliometrics: complementarities and ambivalences in the development and use of indicators—a state-of-the-art report," Scientometrics, Springer;Akadémiai Kiadó, vol. 109(3), pages 2129-2150, December.
    20. Rodrigo Costas & Thomas Franssen, 2018. "Reflections around ‘the cautionary use’ of the h-index: response to Teixeira da Silva and Dobránszki," Scientometrics, Springer;Akadémiai Kiadó, vol. 115(2), pages 1125-1130, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:infome:v:13:y:2019:i:1:p:291-298. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/joi .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.