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
    ---><---

    References listed on IDEAS

    as
    1. Hassan S. Bakouch & Tassaddaq Hussain & Marina Tošić & Vladica S. Stojanović & Najla Qarmalah, 2023. "Unit Exponential Probability Distribution: Characterization and Applications in Environmental and Engineering Data Modeling," Mathematics, MDPI, vol. 11(19), pages 1-22, October.
    2. Francesca Condino & Filippo Domma, 2017. "A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 51-68, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lukun Zheng & Ngoc Nguyen & Peyton Erslan, 2025. "A New Class of Probability Distributions via Half-Elliptical Functions," Mathematics, MDPI, vol. 13(11), pages 1-20, May.
    2. Maria T. Vasileva, 2023. "On Topp-Leone-G Power Series: Saturation in the Hausdorff Sense and Applications," Mathematics, MDPI, vol. 11(22), pages 1-11, November.
    3. Hua Xin & Yuhlong Lio & Ya-Yen Fan & Tzong-Ru Tsai, 2024. "Bias-Correction Methods for the Unit Exponential Distribution and Applications," Mathematics, MDPI, vol. 12(12), pages 1-17, June.
    4. Ishfaq S. Ahmad & Rameesa Jan & Poonam Nirwan & Peer Bilal Ahmad, 2024. "A New Class of Distribution Over Bounded Support and Its Associated Regression Model," Annals of Data Science, Springer, vol. 11(2), pages 549-569, April.
    5. Vladica S. Stojanović & Tanja Jovanović Spasojević & Mihailo Jovanović, 2024. "Laplace-Logistic Unit Distribution with Application in Dynamic and Regression Analysis," Mathematics, MDPI, vol. 12(14), pages 1-21, July.
    6. Komal Shekhawat & Vikas Kumar Sharma, 2021. "An Extension of J-Shaped Distribution with Application to Tissue Damage Proportions in Blood," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 548-574, November.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc 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 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.