Advanced Search
MyIDEAS: Login to save this article or follow this journal

On the extreme order statistics for a stationary sequence


Author Info

  • Hsing, Tailen
Registered author(s):


    Suppose that {[xi]j} is a strictly stationary sequence which satisfies the strong mixing condition. Denote by M(k)n the kth largest value of [xi]1,[xi]2,...,[xi]n, and {[upsilon]n(·)} a sequence of normalizing functions for which P[M(1)n[less-than-or-equals, slant][upsilon]n(x)]converges weakly to a continuous distribution G(x). It is shown that if for some k=2,3,...,P[M(k)n[less-than-or-equals, slant][upsilon]n(x)] converges for each x, then there exist probabilities p1,...,pk-1 such that P[M(j)n[less-than-or-equals, slant][upsilon]n(x)] converges weakly to for j=2,...,k, where natural interpretations can be given for the pj. This generalizes certain results due to Dziubdziela (1984) and Hsing, Hüsler and Leadbetter (1986). It is further demonstrated that, with minor modification, the technique can be extended to study the joint limiting distribution of the order statistics. In particular, Theorem 1 of Welsch (1972) is generalized, and some links between the convergence of the order statistics and that of certain point processes are established.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 29 (1988)
    Issue (Month): 1 ()
    Pages: 155-169

    as in new window
    Handle: RePEc:eee:spapps:v:29:y:1988:i:1:p:155-169

    Contact details of provider:
    Web page:

    Order Information:
    Postal: http://

    Related research

    Keywords: extreme values point processes weak convergence;


    No references listed on IDEAS
    You can help add them by filling out this form.


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

    Cited by:
    1. Novak, S. Y., 2002. "Multilevel clustering of extremes," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 59-75, January.
    2. Davis, Richard A. & Mikosch, Thomas & Zhao, Yuwei, 2013. "Measures of serial extremal dependence and their estimation," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2575-2602.
    3. Hashorva, Enkelejd, 2007. "On the asymptotic distribution of certain bivariate reinsurance treaties," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 200-208, March.
    4. Hashorva, Enkelejd, 2003. "On the number of near-maximum insurance claim under dependence," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 37-49, February.


    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:29:y:1988:i:1:p:155-169. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.