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

Ammar M. Sarhan (), Thamer Manshi and M. E. Sobh
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Ammar M. Sarhan: Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
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

Stats, 2025, vol. 8, issue 3, 1-27

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.

Keywords: statistical distributions; maximum likelihood method; Monte Carlo simulation; data analysis; reliability; statistical inferences (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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