IDEAS home Printed from https://ideas.repec.org/a/spr/scient/v91y2012i1d10.1007_s11192-011-0539-y.html
   My bibliography  Save this article

Theory and practice of the shifted Lotka function

Author

Listed:
  • Leo Egghe

    (Campus Diepenbeek
    Antwerp University (UA), IBW)

  • Ronald Rousseau

    (Antwerp University (UA), IBW
    Faculty of Engineering Technology
    K. U. Leuven)

Abstract

One of the major drawbacks of the classical Lotka function is that arguments only start from the value 1. However, in many applications one may want to start from the value 0, e.g. when including zero received citations. In this article we consider the shifted Lotka function, which includes the case of zero items. Basic results for the total number of sources, the total number of items and the average number of items per source are given in this framework. Next we give the rank-frequency function (Zipf-type function) corresponding to the shifted Lotka function and prove their exact relation. The article ends with a practical example which can be fitted by a shifted Lotka function.

Suggested Citation

  • Leo Egghe & Ronald Rousseau, 2012. "Theory and practice of the shifted Lotka function," Scientometrics, Springer;Akadémiai Kiadó, vol. 91(1), pages 295-301, April.
    • Handle: RePEc:spr:scient:v:91:y:2012:i:1:d:10.1007_s11192-011-0539-y
    DOI: 10.1007/s11192-011-0539-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11192-011-0539-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11192-011-0539-y?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 & Raf Guns & Ronald Rousseau, 2011. "Thoughts on uncitedness: Nobel laureates and Fields medalists as case studies," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 62(8), pages 1637-1644, August.
    2. Leo Egghe & Ronald Rousseau, 2006. "An informetric model for the Hirsch-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 121-129, October.
    3. Leo Egghe & Raf Guns & Ronald Rousseau, 2011. "Thoughts on uncitedness: Nobel laureates and Fields medalists as case studies," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 62(8), pages 1637-1644, August.
    4. Quentin L. Burrell, 2002. "Will this paper ever be cited?," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 53(3), pages 232-235.
    5. Staša Milojević, 2010. "Power law distributions in information science: Making the case for logarithmic binning," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 61(12), pages 2417-2425, December.
    6. Paul Travis Nicholls, 1987. "Estimation of Zipf parameters," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 38(6), pages 443-445, November.
    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. Quentin L. Burrell, 2014. "The individual author’s publication–citation process: theory and practice," Scientometrics, Springer;Akadémiai Kiadó, vol. 98(1), pages 725-742, January.
    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. Cena, Anna & Gagolewski, Marek & Siudem, Grzegorz & Żogała-Siudem, Barbara, 2022. "Validating citation models by proxy indices," Journal of Informetrics, Elsevier, vol. 16(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. Bertoli-Barsotti, Lucio & Lando, Tommaso, 2015. "On a formula for the h-index," Journal of Informetrics, Elsevier, vol. 9(4), pages 762-776.
    2. 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.
    3. Quentin L. Burrell, 2012. "Alternative thoughts on uncitedness," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 63(7), pages 1466-1470, July.
    4. Quentin L. Burrell, 2014. "The individual author’s publication–citation process: theory and practice," Scientometrics, Springer;Akadémiai Kiadó, vol. 98(1), pages 725-742, January.
    5. Agnieszka Geras & Grzegorz Siudem & Marek Gagolewski, 2022. "Time to vote: Temporal clustering of user activity on Stack Overflow," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 73(12), pages 1681-1691, December.
    6. Helena H. Zhang & Fred Y. Ye, 2020. "Identifying ‘associated-sleeping-beauties’ in ‘swan-groups’ based on small qualified datasets of physics and economics," Scientometrics, Springer;Akadémiai Kiadó, vol. 122(3), pages 1525-1537, March.
    7. 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.
    8. Liang, Liming & Zhong, Zhen & Rousseau, Ronald, 2015. "Uncited papers, uncited authors and uncited topics: A case study in library and information science," Journal of Informetrics, Elsevier, vol. 9(1), pages 50-58.
    9. Lucy Amez, 2012. "Citation measures at the micro level: Influence of publication age, field, and uncitedness," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 63(7), pages 1459-1465, July.
    10. Jianhua Hou & Xiucai Yang, 2019. "Patent sleeping beauties: evolutionary trajectories and identification methods," Scientometrics, Springer;Akadémiai Kiadó, vol. 120(1), pages 187-215, July.
    11. Shaibu Mohammed & Anthony Morgan & Emmanuel Nyantakyi, 2020. "On the influence of uncited publications on a researcher’s h-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 122(3), pages 1791-1799, March.
    12. Jiang Li & Fred Y. Ye, 2012. "The phenomenon of all-elements-sleeping-beauties in scientific literature," Scientometrics, Springer;Akadémiai Kiadó, vol. 92(3), pages 795-799, September.
    13. Jianhua Hou & Hao Li & Yang Zhang, 2023. "Altmetrics-based sleeping beauties: necessity or just a supplement?," Scientometrics, Springer;Akadémiai Kiadó, vol. 128(10), pages 5477-5506, October.
    14. Ronald Rousseau & Xiaojun Hu, 2018. "Under-cited influential work by Eugene Garfield," Scientometrics, Springer;Akadémiai Kiadó, vol. 114(2), pages 651-657, February.
    15. Egghe, Leo & Rousseau, Ronald, 2023. "Global informetric impact: A description and definition using bundles," Journal of Informetrics, Elsevier, vol. 17(1).
    16. Jianhua Hou & Jiantao Ye, 2020. "Are uncited papers necessarily all nonimpact papers? A quantitative analysis," Scientometrics, Springer;Akadémiai Kiadó, vol. 124(2), pages 1631-1662, August.
    17. Elisabeth Maria Schlagberger & Lutz Bornmann & Johann Bauer, 2016. "At what institutions did Nobel laureates do their prize-winning work? An analysis of biographical information on Nobel laureates from 1994 to 2014," Scientometrics, Springer;Akadémiai Kiadó, vol. 109(2), pages 723-767, November.
    18. Zhao, Star X. & Tan, Alice M. & Yu, Shuang & Xu, Xin, 2018. "Analyzing the research funding in physics: The perspective of production and collaboration at institution level," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 662-674.
    19. Jeppe Nicolaisen & Tove Faber Frandsen, 2019. "Zero impact: a large-scale study of uncitedness," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(2), pages 1227-1254, May.
    20. Li, Jiang & Shi, Dongbo & Zhao, Star X. & Ye, Fred Y., 2014. "A study of the “heartbeat spectra” for “sleeping beauties”," Journal of Informetrics, Elsevier, vol. 8(3), pages 493-502.

    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:spr:scient:v:91:y:2012:i:1:d:10.1007_s11192-011-0539-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.