A NEW FAMILY OF UNIT-DISTRIBUTIONS: DEFINITION, PROPERTIES AND APPLICATIONS

A NEW FAMILY OF UNIT-DISTRIBUTIONS: DEFINITION, PROPERTIES AND APPLICATIONS

T. Arslan

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Abstract

In this study, a new family of unit-distributions is introduced. Then, a unit- Gumbel 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 de ning 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.

Keywords

Beta distribution, a family of unit-distributions, Kumaraswamy distribution, maximum likelihood method, unit-Gumbel distribution.