Alpha Power Transformed Generalized Weibull Distribution With Its Detailed Properties and Applications

This study introduces the alpha power transformed generalized Weibull distribution (APTGWD), a novel probability model derived by transforming the generalization of Weibull distribution (GWD) using an alpha power technique. Various shapes of the distribution, including probability, cumulative, hazard, and survival functions, are explored. Noteworthy hazard rate function shapes such as increasing, decreasing, bathtub, and bumping curves are revealed. Key properties such as the quantile function, moments, and moment generating function (MGF) are derived, showcasing the distribution’s versatility in modeling both monotone and nonmonotone hazard rate functions common in reliability and lifetime data analysis. Parameter estimation is performed using the maximum likelihood method. Simulation studies and analysis of real datasets with the new APTGWD model demonstrate the distribution’s potential as an alternative for modeling lifetime and reliability data. The study presents a new probability distribution with interesting properties, contributing to statistical theory. Implications for statistical inferences, parameter estimation, and applications in fields of life sciences are discussed, offering new insights. This finding can help as a foundation for future studies in statistics and related areas.