IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0163241.html
   My bibliography  Save this article

Beyond Zipf’s Law: The Lavalette Rank Function and Its Properties

Author

Listed:
  • Oscar Fontanelli
  • Pedro Miramontes
  • Yaning Yang
  • Germinal Cocho
  • Wentian Li

Abstract

Although Zipf’s law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf’s law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf’s law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.

Suggested Citation

  • Oscar Fontanelli & Pedro Miramontes & Yaning Yang & Germinal Cocho & Wentian Li, 2016. "Beyond Zipf’s Law: The Lavalette Rank Function and Its Properties," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-14, September.
    • Handle: RePEc:plo:pone00:0163241
    DOI: 10.1371/journal.pone.0163241
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0163241
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0163241&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0163241?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
    ---><---

    References listed on IDEAS

    as
    1. Petersen, Alexander M. & Succi, Sauro, 2013. "The Z-index: A geometric representation of productivity and impact which accounts for information in the entire rank-citation profile," Journal of Informetrics, Elsevier, vol. 7(4), pages 823-832.
    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. Patrick Erik Bradley & Martin Behnisch, 2019. "Heavy-tailed distributions for building stock data," Environment and Planning B, , vol. 46(7), pages 1281-1296, September.

    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. Letchford, Adrian & Preis, Tobias & Moat, Helen Susannah, 2016. "The advantage of simple paper abstracts," Journal of Informetrics, Elsevier, vol. 10(1), pages 1-8.
    2. Fabio Zagonari, 2019. "Scientific Production and Productivity for Characterizing an Author’s Publication History: Simple and Nested Gini’s and Hirsch’s Indexes Combined," Publications, MDPI, vol. 7(2), pages 1-30, May.
    3. Rossi, Luciano & Freire, Igor L. & Mena-Chalco, Jesús P., 2017. "Genealogical index: A metric to analyze advisor–advisee relationships," Journal of Informetrics, Elsevier, vol. 11(2), pages 564-582.

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0163241. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.