The New Generalized Exponentiated Fréchet–Weibull Distribution: Properties, Applications, and Regression Model

Statistical probability distributions are commonly used by data analysts and statisticians to describe and analyze their data. It is possible in many situations that data would not fit the existing classical distributions. A new distribution is therefore required in order to accommodate the complexities of different data shapes and enhance the goodness of fit. A novel model called the new generalized exponentiated Fréchet–Weibull distribution is proposed in this paper by combing two methods, the transformed transformer method and the new generalized exponentiated method. This novel modeling approach is capable of modeling complex data structures in a wide range of applications. Some statistical properties of the new distribution are derived. The parameters have been estimated using the method of maximum likelihood. Then, different simulation studies have been conducted to assess the behavior of the estimators. The performance of the proposed distribution in modeling has been investigated by means of applications to three real datasets. Further, a new regression model is proposed through reparametrization of the new generalized exponentiated Fréchet–Weibull distribution using the log-location-scale technique. The effectiveness of the proposed regression model is also investigated with two simulation studies and three real censored datasets. The results demonstrated the superiority of the proposed models over other competing models.