A novel extension to the unit Weibull distribution: properties and inference with applications to medicine, engineering, and radiation

Hassan Eid Elghaly; Mohamed A. Abd Elgawad; Boping Tian; Hassan Eid Elghaly; Mohamed A. Abd Elgawad; Boping Tian

doi:10.3934/math.2025837

AIMS Mathematics

2025, Volume 10, Issue 8: 18731-18769. doi: 10.3934/math.2025837

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A novel extension to the unit Weibull distribution: properties and inference with applications to medicine, engineering, and radiation

1.
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2.
Department of Applied Statistics and Insurance, Faculty of Commerce, Mansoura University, Mansoura 35516, Egypt
3.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; moaasalem@imamu.edu.sa

Received: 18 June 2025 Revised: 02 August 2025 Accepted: 05 August 2025 Published: 19 August 2025
MSC : 60E05, 62G05, 62N05

This study introduces a new extension of the unit Weibull distribution called the unit power generalized Weibull distribution (UPGWD). The UPGWD arises from inverse exponential function transformation of the power generalized Weibull distribution. It is a highly competitive distribution compared with the existing unit distributions in the literature, offering significant flexibility. The probability density function of the UPGWD can display several forms, including constant, bathtub, unimodal, J-shaped (increasing), and inverted J-shaped (decreasing) configurations. Conversely, its hazard function may exhibit increasing J-shaped and bathtub configurations. Some of its corresponding basic statistical and reliability properties are introduced. Furthermore, the maximum likelihood estimation (MLE) technique is applied to estimate its parameters. A Monte Carlo simulation study is performed to assess the accuracy of the MLE estimates. Finally, to demonstrate the potential importance of the UPGWD, four applications with actual lifetime data related to COVID-19, reliability, engineering, and radiation are discussed. The empirical application further validated its efficacy, surpassing the earlier existing unit Weibull distributions, including the unit Weibull, the unit inverted exponentiated Weibull, the upper truncated Weibull, the bounded exponentiated Weibull, the power upper truncated Weibull, and the Poisson unit Weibull distributions.
- Weibull distribution,
- unit distributions,
- reliability,
- survival function,
- bathtub-shaped,
- stress–strength reliability,
- maximum likelihood estimation,
- Monte Carlo simulation
Citation: Hassan Eid Elghaly, Mohamed A. Abd Elgawad, Boping Tian. A novel extension to the unit Weibull distribution: properties and inference with applications to medicine, engineering, and radiation[J]. AIMS Mathematics, 2025, 10(8): 18731-18769. doi: 10.3934/math.2025837

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Abstract

This study introduces a new extension of the unit Weibull distribution called the unit power generalized Weibull distribution (UPGWD). The UPGWD arises from inverse exponential function transformation of the power generalized Weibull distribution. It is a highly competitive distribution compared with the existing unit distributions in the literature, offering significant flexibility. The probability density function of the UPGWD can display several forms, including constant, bathtub, unimodal, J-shaped (increasing), and inverted J-shaped (decreasing) configurations. Conversely, its hazard function may exhibit increasing J-shaped and bathtub configurations. Some of its corresponding basic statistical and reliability properties are introduced. Furthermore, the maximum likelihood estimation (MLE) technique is applied to estimate its parameters. A Monte Carlo simulation study is performed to assess the accuracy of the MLE estimates. Finally, to demonstrate the potential importance of the UPGWD, four applications with actual lifetime data related to COVID-19, reliability, engineering, and radiation are discussed. The empirical application further validated its efficacy, surpassing the earlier existing unit Weibull distributions, including the unit Weibull, the unit inverted exponentiated Weibull, the upper truncated Weibull, the bounded exponentiated Weibull, the power upper truncated Weibull, and the Poisson unit Weibull distributions.

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