A flexible extension of the unit upper truncated Weibull distribution: Statistical analysis with applications on geology, engineering, and radiation Data

A new extension of the unit upper truncated Weibull (UUTW) probability distribution termed power upper truncated probability distribution (PUTWD) has been developed through power transformation to address the limitations of the existing statistical distributions in capturing complex data patterns. The study derives key statistical properties for the PUTWD. Furthermore, parameter estimation is conducted using various methods. Monte Carlo simulations evaluated the performance of these estimation methods, revealing improved accuracy and consistency with increasing sample size. The PUTWD's flexibility and superiority are demonstrated through applications to diverse real-world datasets, including petroleum reserve outputs, flood level measurements, engineering reliability, the COVID-19 pandemic, and radiation, showcasing its dominance over existing distributions and enhancing statistical modeling capabilities.