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A Flexible Location-Scale Burr XII Distribution with Applications in Cancer and Glass Fiber Data
* 1 , 2 , 1 , 1 , 1 , 1 , 3
1  Department of Statistics, Ahmadu Bello University, Zaria 810107, Nigeria
2  School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, China
3  Department of Statistics, Aliko Dangote University of Science and Technology, Wudil 713281, Nigeria
Academic Editor: Antonio Di Crescenzo

Abstract:

Accurate statistical modeling of lifetime and reliability data remains a significant challenge in fields such as survival analysis, engineering, and environmental studies, particularly when datasets exhibit varying skewness, heavy tails, and complex hazard rate structures. Classical distributions, including the Burr XII model, often demonstrate limited flexibility in capturing diverse distributional shapes and hazard behaviors observed in real-world data. In this study, a new and flexible distribution, referred to as the Location-Scale Burr XII (LS-Burr XII) distribution, is introduced by adding a location-scale transformation into the classical Burr XII model. The LS-Burr XII distribution captures a wide range of density shapes, including right-skewed, left-skewed, bell-shaped, J-shaped, and reversed J-shaped forms. It also accommodates diverse hazard rate behaviors, including increasing, decreasing, constant, bathtub, unimodal, and modified bathtub shapes. These features extend beyond the capabilities of the classical Burr XII distribution and many of its existing extensions. Several statistical properties of the proposed model are derived, including the quantile function, moments, moment generating function, and order statistics. Parameter estimation is carried out using the maximum likelihood method, and a Monte Carlo simulation study is conducted to assess the performance of the estimators. The practical usefulness of the proposed model is demonstrated using two real-world datasets, including leukemia cancer data from Saudi Arabia and glass fiber strength data obtained from the UK National Physical Laboratory. The performance of the proposed LS-Burr XII distribution is compared with the classical Burr XII model and other existing extensions using standard goodness-of-fit criteria. The results indicate that the proposed model offers greater flexibility and provides a better fit with the observed data. These findings suggest that the LS-Burr XII distribution offers a useful and competitive alternative for modeling complex lifetime data in reliability and biomedical applications.

Keywords: Statistical distribution; Location-Scale transformation; Moments; Parameter estimation; Lifetime data; Hazard function

 
 
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