A New Family of Generalized Distributions on the Unit Interval: The T− kumasatwamy Family of Distributions

Abstract

The so-called Kumaraswamy distribution is a special probability distribution developed to model doubled bounded random processes for which the mode do not necessarily have to be within the bounds. In this article, a generalization of the Kumaraswamy distribution called the T-Kumaraswamy family is defined using the T-R {Y} family of distributions framework. The resulting T-Kumaraswamy family is obtained using the quantile functions of some standardized distributions. Some general mathematical properties of the new family are studied. Five new generalized Kumaraswamy distributions are proposed using the T-Kumaraswamy method. Real data sets are further used to test the applicability of the new family.

The Generalized Distributions on the Unit Interval based on the T-Topp-Leone Family of Distributions

“…We can notice that the popular unit distribution such as beta, Kumaraswamy, and TL distributions have been used to generate the lifetime distribution in many researchers. Although there are researches tried to develop the generalized distribution with support on such as the T-Kumaraswamy family of distributions which has the members of family called generalized Kumaraswamy distributions introduced by Osatohanmwen et al [18], the number of new unit distributions rarely find compared to the number of new lifetime distributions.…”