Alpha Power Transformed Fr ´echet Distribution

Abstract

The Fr´echet distribution has several applications in different fields of study and is most commonly used for modeling extreme events. In recent time, modifications of the Fr´echet distribution have been proposed to improve its fit when used for modeling lifetime data. In this paper, a new modification called the alpha power transformed Fr´echet distribution is proposed and studied. The parameters of the model are estimated using maximum-likelihood estimation and simulation studies are performed to investigate the properties of the estimators for the parameters. Applications of the model are demonstrated using two-real data sets. Finally, bivariate and multivariate extensions of the model are proposed using copulas.