IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v16y1993i1p39-41.html
   My bibliography  Save this article

Equivalence of Hartley--David--Gumbel and Papathanasiou bounds and some further remarks

Author

Listed:
  • Balakrishnan, N.
  • Balasubramanian, K.

Abstract

Let X1:2, X2:2 be the order statistics of a sample of size two from an absolutely continuous distribution F with finite variance. In this note, we show that the upper bound for Cov(X1:2, X2:2) (and the associated characterization of the uniform distribution) established recently by Papathanasiou (1990) is equivalent to the well-known upper bound for E(X2:2) due to Hartley and David (1954) and Gumbel (1954). This simple argument is also shown to yield immediately the generalized bound of Ma Chunsheng (1992). Some further remarks with regard to extensions are made.

Suggested Citation

  • Balakrishnan, N. & Balasubramanian, K., 1993. "Equivalence of Hartley--David--Gumbel and Papathanasiou bounds and some further remarks," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 39-41, January.
    • Handle: RePEc:eee:stapro:v:16:y:1993:i:1:p:39-41
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0167-7152(93)90119-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marek Beśka & Krzysztof Jasiński & Tomasz Rychlik & Marcin Spryszyński, 2012. "Mixed systems with minimal and maximal lifetime variances," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 877-894, October.
    2. Navarro, Jorge & Balakrishnan, N., 2010. "Study of some measures of dependence between order statistics and systems," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 52-67, January.

    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:eee:stapro:v:16:y:1993:i:1:p:39-41. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.