A new extended Fréchet model with different estimation methods and applications

In this study, we introduce a new extension of the Fréchet distribution known as the new extended Fréchet (NE_Fr) model. The NE_Fr is created by combining the new extended <i>X</i> family of distributions and the Fréchet distribution. The NE_Fr has more flexibility than the classical Fréchet distribution and some generalizations of the Fréchet distribution. The probability density function of the NE_Fr can be decreasing, unimodal and right skewed shape but it's hazard rate function can be decreasing or up-side-down shape. Several mathematical properties of the new model were derived by calculating the quantile function, the ordinary moments, the incomplete moments, the moment generating function, the conditional moment, the Bonferroni curve and the Lorenz curve. Several entropy measures were developed for this purpose. The inferences from the NE_Fr distribution were investigated using several established methods such as maximum likelihood estimation, least squares and weighted least squares estimation, and Anderson-Darling estimation. The simulation results demonstrated the computational efficiency of these techniques. The proposed NE_Fr distribution was demonstrated to be useful by examining three actual data sets.