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

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.