Some Generalizations of the Type II Half Logistic Topp-Leone Distributions

Abstract

We present three new extensions of the Type II Half Logistic Topp-Leone-G (TIIHLTL-G) distribution: the Type II Half Logistic Topp-Leone-G Power Series (TIIHLTL-GPS) distribution, the Beta Type II Half Logistic Topp-Leone-G (BTIIHLTL-G) distribution and the Type II Half Logistic Topp-Leone Exponentiated Generalized-G (TIIHLTLEG-G) distribution. We are motivated by the frequent failure of classical statistical distributions in offering a good fit to actual data which is particularly due to their lack of flexibility. Statistical properties of the new distributions are explored, methods of finding estimators such as the Maximum Likelihood were used and we also assessed the performance of the distributions by carrying out a simulation study for the special cases of each distribution. Finally, we applied our distributions to real data sets to show that they are useful when applied to real data. We conclude that the new distributions offer a good fit in comparison to some existing methods and improve the flexibility of some classical distributions.