On Unit J-Shaped Distributions: Properties and Estimation with Applications

Authors

• Asmaa S. Al-Moisheer Prof., Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaFollow
• Khalaf S. Sultan Prof., Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt
• Mahmoud MansourFollow

Document Type

Article

Publication Date

Winter 3-17-2026

Abstract

This study is a detailed study of unit J-shaped distributions which establishes and examines the unit Topp–Leone distribution. The proposed study presents a mathematically tractable model of bounded data with strong skewness and boundary effects. Various basic distributional properties, such as moments, entropy measures, order statistics, and L-moments, are obtained in explicit form, which provides a full analytic description of the model. Type-II censoring is applied to develop some statistical inferential methods. The usefulness of the suggested distribution is illustrated by the application to the normalized water use efficiency indicators and censored survival time data. The findings are useful to the theory of unit distributions, as they introduce new analytics that have been demonstrated to be beneficial in practice and demonstrate that the theory is effective in applications with limited and censored data.

Recommended Citation

Al-Moisheer, A. S., Sultan, K. S., & Mansour, M. M. M. (2026). On Unit J-Shaped Distributions: Properties and Estimation with Applications. Mathematics, 14(6), 1021. https://doi.org/10.3390/math14061021