IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v19y2017i1d10.1007_s11009-016-9481-z.html
   My bibliography  Save this article

Bivariate Binomial Moments and Bonferroni-Type Inequalities

Author

Listed:
  • Qin Ding

    (FO7, University of Sydney)

  • Eugene Seneta

    (FO7, University of Sydney)

Abstract

We obtain bivariate forms of Gumbel’s, Fréchet’s and Chung’s linear inequalities for P(S ≥ u, T ≥ v) in terms of the bivariate binomial moments {S i, j }, 1 ≤ i ≤ k,1 ≤ j ≤ l of the joint distribution of (S, T). At u = v = 1, the Gumbel and Fréchet bounds improve monotonically with non-decreasing (k, l). The method of proof uses combinatorial identities, and reveals a multiplicative structure before taking expectation over sample points.

Suggested Citation

  • Qin Ding & Eugene Seneta, 2017. "Bivariate Binomial Moments and Bonferroni-Type Inequalities," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 331-348, March.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:1:d:10.1007_s11009-016-9481-z
    DOI: 10.1007/s11009-016-9481-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-016-9481-z
    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/s11009-016-9481-z?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. Fred M. Hoppe & Eugene Seneta, 2012. "Gumbel’s Identity, Binomial Moments, and Bonferroni Sums," International Statistical Review, International Statistical Institute, vol. 80(2), pages 269-292, August.
    2. Galambos, J. & Xu, Y., 1995. "Bivariate Extension of the Method of Polynomials for Bonferroni-Type Inequalities," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 131-139, January.
    3. Chen, Tuhao & Seneta, E., 1995. "A note on bivariate Dawson-Sankoff-type bounds," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 99-104, August.
    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. Barakat, H.M., 2009. "Multivariate order statistics based on dependent and nonidentically distributed random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 81-90, January.
    2. Simonelli, Italo, 1999. "An Extension of the Bivariate Method of Polynomials and a Reduction Formula for Bonferroni-Type Inequalities," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 1-9, April.

    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:metcap:v:19:y:2017:i:1:d:10.1007_s11009-016-9481-z. 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.