IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v8y2025i3p81-d1748287.html
   My bibliography  Save this article

The Unit-Modified Weibull Distribution: Theory, Estimation, and Real-World Applications

Author

Listed:
  • Ammar M. Sarhan

    (Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Department of Mathematics and Statistics, Dalhousie University, Halifax, NS B3H 4R2, Canada)

  • Thamer Manshi

    (Department of Statistics & Operation Research, College of science, King Saud University, Riyadh P.O. Box 11451, Saudi Arabia)

  • M. E. Sobh

    (Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

This paper introduces the Unit-Modified Weibull (UMW) distribution, a novel probability model defined on the unit interval ( 0 , 1 ) . We derive its key statistical properties and estimate its parameters using the maximum likelihood method. The performance of the estimators is assessed via a simulation study based on mean squared error, coverage probability, and average confidence interval length. To evaluate the practical utility of the model, we analyze three real-world data sets. Both parametric and nonparametric goodness-of-fit techniques are employed to compare the UMW distribution with several well-established competing models. In addition, nonparametric diagnostic tools such as total time on test transform plots and violin plots are used to explore the data’s behavior and assess the adequacy of the proposed model. Results indicate that the UMW distribution offers a competitive and flexible alternative for modeling bounded data.

Suggested Citation

  • Ammar M. Sarhan & Thamer Manshi & M. E. Sobh, 2025. "The Unit-Modified Weibull Distribution: Theory, Estimation, and Real-World Applications," Stats, MDPI, vol. 8(3), pages 1-27, September.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:3:p:81-:d:1748287
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/8/3/81/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/8/3/81/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:jstats:v:8:y:2025:i:3:p:81-:d:1748287. 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.