IDEAS home Printed from
   My bibliography  Save this article

Bivariate Distribution and Hazard Functions When a Component is Randomly Truncated


  • Gürler, Ülkü


In random truncation models one observes the i.i.d. pairs (Ti[less-than-or-equals, slant]Yi),i=1, ..., n. IfYis the variable of interest, thenTis another independent variable which prevents the complete observation ofYand random left truncation occurs. Such a type of incomplete data is encountered in medical studies as well as in economy, astronomy, and insurance applications. Let (Y, Y) be a bivariate vector of random variables with joint distribution functionF(y, x) and suppose the variableYis randomly truncated from the left. In this study, nonparametric estimators for the bivariate distribution and hazard functions are considered. A nonparametric estimator forF(y, x) is proposed and an a.s. representation is obtained. This representation is used to establish the consistency and the weak convergence of the empirical process. An expression for the variance of the asymptotic distribution is presented and an estimator is proposed. Bivariate "diverse-hazard" vector is introduced whic h captures the individual and joint failure behaviors of the random variables in opposite "time" directions. Estimators for this vector are presented and the large sample properties are discussed. Possible applications and a moderate size simulation study are also presented.

Suggested Citation

  • Gürler, Ülkü, 1997. "Bivariate Distribution and Hazard Functions When a Component is Randomly Truncated," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 20-47, January.
  • Handle: RePEc:eee:jmvana:v:60:y:1997:i:1:p:20-47

    Download full text from publisher

    File URL:
    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.


    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:jmvana:v:60:y:1997:i:1:p:20-47. 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). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.