IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-94-011-5532-8_15.html
   My bibliography  Save this book chapter

Diagonal Copulas

In: Distributions with given Marginals and Moment Problems

Author

Listed:
  • Roger B. Nelsen

    (Lewis & Clark College)

  • Gregory A. Fredricks

    (Lewis & Clark College)

Abstract

A diagonal copula has the form K(u,υ) = min(u, υ,(1/2)[δ(u) + δ(υ)]) where δ is any function satisfying (i) δ(1) = 1; (ii) 0 ≤ δ(t 2) - δ(t 1) ≤ 2(t 2 - t 1) for all t 1, t 2 in [0,1] with t 1 ≤ t 2; and (iii) δ(t) ≤ t for all t ∈ [0,1]. A diagonal copula is an ordinal sum of Min and what we call quasi-hairpin copulas, and conversely. Diagonal copulas are symmetric, singular and extremal. We relate them to shuffles of Min and copulas with hairpin support, and prove the following characterization theorem: Suppose X and Y are continuous random variables with copula C and a common marginal distribution function. Then the joint distribution function of max(X,Y) and min(X, Y) is the Fréchet upper bound if and only if C is a diagonal copula.

Suggested Citation

  • Roger B. Nelsen & Gregory A. Fredricks, 1997. "Diagonal Copulas," Springer Books, in: Viktor Beneš & Josef Štěpán (ed.), Distributions with given Marginals and Moment Problems, pages 121-128, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5532-8_15
    DOI: 10.1007/978-94-011-5532-8_15
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    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:spr:sprchp:978-94-011-5532-8_15. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.