IDEAS home Printed from https://ideas.repec.org/a/vrs/demode/v11y2023i1p14n1.html
   My bibliography  Save this article

A link between Kendall’s τ, the length measure and the surface of bivariate copulas, and a consequence to copulas with self-similar support

Author

Listed:
  • Sánchez Juan Fernández

    (Grupo de Investigación de Análisis Matemático, Universidad de Almería, 04120 La Cañada de San Urbano, Almería, Spain)

  • Trutschnig Wolfgang

    (Department for Artificial Intelligence & Human Interfaces, University of Salzburg, Hellbrunnerstrasse 34, 5020 Salzburg, Austria)

Abstract

Working with shuffles, we establish a close link between Kendall’s τ \tau , the so-called length measure, and the surface area of bivariate copulas and derive some consequences. While it is well known that Spearman’s ρ \rho of a bivariate copula A A is a rescaled version of the volume of the area under the graph of A A , in this contribution we show that the other famous concordance measure, Kendall’s τ \tau , allows for a simple geometric interpretation as well – it is inextricably linked to the surface area of A A .

Suggested Citation

  • Sánchez Juan Fernández & Trutschnig Wolfgang, 2023. "A link between Kendall’s τ, the length measure and the surface of bivariate copulas, and a consequence to copulas with self-similar support," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-14, January.
    • Handle: RePEc:vrs:demode:v:11:y:2023:i:1:p:14:n:1
    DOI: 10.1515/demo-2023-0105
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/demo-2023-0105
    Download Restriction: no
    File URL: https://libkey.io/10.1515/demo-2023-0105?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. Coblenz, Maximilian & Grothe, Oliver & Schreyer, Manuela & Trutschnig, Wolfgang, 2018. "On the length of copula level curves," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 347-365.
    2. Fredricks, Gregory A. & Nelsen, Roger B. & Rodriguez-Lallena, Jose Antonio, 2005. "Copulas with fractal supports," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 42-48, August.
    3. Juan Fernández Sánchez & Wolfgang Trutschnig, 2015. "Conditioning-based metrics on the space of multivariate copulas and their interrelation with uniform and levelwise convergence and Iterated Function Systems," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1311-1336, December.
    Full references (including those not matched with items on IDEAS)

    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. Siburg, Karl Friedrich & Stoimenov, Pavel A., 2007. "Gluing copulas," Technical Reports 2007,31, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Trutschnig, Wolfgang, 2013. "On Cesáro convergence of iterates of the star product of copulas," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 357-365.
    3. Henryk Zähle, 2022. "A concept of copula robustness and its applications in quantitative risk management," Finance and Stochastics, Springer, vol. 26(4), pages 825-875, October.
    4. Griessenberger Florian & Trutschnig Wolfgang, 2022. "Maximal asymmetry of bivariate copulas and consequences to measures of dependence," Dependence Modeling, De Gruyter, vol. 10(1), pages 245-269, January.
    5. Fabrizio Durante & Juan Fernández Sánchez & Wolfgang Trutschnig, 2020. "Spatially homogeneous copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 607-626, April.
    6. Juan Fernández Sánchez & Wolfgang Trutschnig, 2015. "Conditioning-based metrics on the space of multivariate copulas and their interrelation with uniform and levelwise convergence and Iterated Function Systems," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1311-1336, December.

    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:vrs:demode:v:11:y:2023:i:1:p:14:n:1. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.