A New Family of Unit-Distributions: Definition, Properties and Applications

Abstract

In this study, a new family of unit-distributions is introduced. Then, a unitGumbel distribution, member of the proposed family of unit-distributions, is obtained as an example, and some of its statistical properties are provided. The maximum likelihood method is used for estimating the shape parameter of the unit-Gumbel distribution. In addition, a new family of continuous distributions is defining by using the composition technique. Finally, real data sets are used for modeling purposes. The result shows that the unit-Gumbel distribution is preferable over some well-known unit-distributions such as the beta, Kumaraswamy, and Topp-Leone, and also the unit-Gompertz distribution, which is recently introduced.