IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Stochastic orderings between distributions and their sample spacings - II

Listed author(s):
  • Khaledi, Baha-Eldin
  • Kochar, Subhash
Registered author(s):

    Let X1:n[less-than-or-equals, slant]X2:n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn:n denote the order statistics of a random sample of size n from a probability distribution with distribution function F. Similarly, let Y1:m[less-than-or-equals, slant]Y2:m[less-than-or-equals, slant]...[less-than-or-equals, slant]Ym:m denote the order statistics of an independent random sample of size m from another distribution with distribution function G. We assume that F and G are absolutely continuous with common support (0,[infinity]). The corresponding normalized spacings are defined by Ui:n[reverse not equivalent](n-i+1)(Xi:n-Xi-1:n) and Vj:m[reverse not equivalent](m-j+1)(Yj:m-Yj-1:m), for i=1,...,n and j=1,...,m, where X0:n=Y0:n[reverse not equivalent]0. It is proved that if X is smaller than Y in the hazard rate order sense and if either F or G is a decreasing failure rate (DFR) distribution, then Ui:n is stochastically smaller than Vj:m for i[less-than-or-equals, slant]j and n-i[greater-or-equal, slanted]m-j. If instead, we assume that X is smaller than Y in the likelihood ratio order and if either F or G is DFR, then this result can be strengthened from stochastic ordering to hazard rate ordering. Finally, under a stronger assumption on the shapes of the distributions that either F or G has log-convex density, it is proved that X being smaller than Y in the likelihood ratio order implies that Ui:n is smaller than Vj:m in the sense of likelihood ratio ordering for i[less-than-or-equals, slant]j and n-i=m-j.

    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.

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 44 (1999)
    Issue (Month): 2 (August)
    Pages: 161-166

    in new window

    Handle: RePEc:eee:stapro:v:44:y:1999:i:2:p:161-166
    Contact details of provider: Web page:

    Order Information: Postal:

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

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

    When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:44:y:1999:i:2:p:161-166. 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: (Dana Niculescu)

    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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.