IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i11p1760-d1409366.html
   My bibliography  Save this article

Change Point Test for Length-Biased Lognormal Distribution under Random Right Censoring

Author

Listed:
  • Mei Li

    (Faculty of Science, Kunming University of Scicence and Technology, Kunming 650500, China)

  • Wei Ning

    (Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA)

  • Yubin Tian

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

Abstract

The length-biased lognormal distribution is a length-biased version of lognormal distribution, which is developed to model the length-biased lifetime data from, for example, biological investigation, medical research, and engineering fields. Owing to the existence of censoring phenomena in lifetime data, we study the change-point-testing problem of length-biased lognormal distribution under random censoring in this paper. A procedure based on the modified information criterion is developed to detect changes in parameters of this distribution. Under the sufficient condition of the Fisher information matrix being positive definite, it is proven that the null asymptotic distribution of the test statistic follows a chi-square distribution. In order to evaluate the uncertainty of change point location estimation, a way of calculating the coverage probabilities and average lengths of confidence sets of change point location based on the profile likelihood and deviation function is proposed. The simulations are conducted, under the scenarios of uniform censoring and exponential censoring, to investigate the validity of the proposed method. And the results indicate that the proposed approach performs better in terms of test power, coverage probabilities, and average lengths of confidence sets compared to the method based on the likelihood ratio test. Subsequently, the proposed approach is applied to the analysis of survival data from heart transplant patients, and the results show that there are differences in the median survival time post-heart transplantation among patients of different ages.

Suggested Citation

  • Mei Li & Wei Ning & Yubin Tian, 2024. "Change Point Test for Length-Biased Lognormal Distribution under Random Right Censoring," Mathematics, MDPI, vol. 12(11), pages 1-20, June.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1760-:d:1409366
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/11/1760/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/11/1760/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:12:y:2024:i:11:p:1760-:d:1409366. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.