The Beta Topp-Leone Generated Family of Distributions and Theirs Applications

Abstract

This work aims to establish a new family of distributions, namely the beta Topp-Leone generated family of distributions. The proposed family of distributions is combined from two families: the beta generated family and the Topp-Leone generated family. Some statistical properties of the proposed family are derived, e.g., linear representation, ordinary moments, and moment generating function. Furthermore, a new modification of Weibull distribution, namely the beta Topp-Leone Weibull distribution, is studied. The beta Topp-Leone Weibull distribution has flexible hazard shapes. Some statistical properties of the proposed distribution are studied, e.g., transformation, quantile function, ordinary moments, and moment generating function. The distribution parameters are estimated with the methods of maximum likelihood estimation. The proposed distribution shows more appropriate than other candidate distributions for fitting with the complete and censored datasets based on the values of Akaike’s information criterion, Bayesian information criterion, Akaike’s information corrected criterion, and Hannon and Quinn’s information criterion.