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

A note on exponential dispersion models which are invariant under length-biased sampling

Listed author(s):
  • Bar-Lev, Shaul K.
  • Van der Duyn Schouten, Frank A.
Registered author(s):

    Length-biased sampling (LBS) situations may occur in clinical trials, reliability, queueing models, survival analysis and population studies where a proper sampling frame is absent. In such situations items are sampled at rate proportional to their "length" so that larger values of the quantity being measured are sampled with higher probabilities. More specifically, if f(x) is a p.d.f. presenting a parent population composed of non-negative valued items then the sample is practically drawn from a distribution with p.d.f. g(x)=xf(x)/E(X) describing the length-biased population. In this case the distribution associated with g is termed a length-biased distribution. In this note, we present a unified approach for characterizing exponential dispersion models which are invariant, up to translations, under various types of LBS. The approach is rather simple as it reduces such invariance problems into differential equations in terms of the derivatives of the associated variance functions.

    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): 70 (2004)
    Issue (Month): 4 (December)
    Pages: 275-284

    in new window

    Handle: RePEc:eee:stapro:v:70:y:2004:i:4:p:275-284
    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:70:y:2004:i:4:p:275-284. 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.