The Kumaraswamy-Generalized Exponentiated Pareto Distribution

Abstract
Based on the Kumaraswamy distribution Jones^{]12 [}, we study the so-called Kum-generalized Exponentiated Pareto distribution that is capable of modeling bathtub-shaped hazard rate functions. For the first time the Kum-GEP distribution is introduced and studied. This distribution can have a decreasing and upside-down bathtub failure rate function depending on the value of its parameters; it's including some special sub-model like exponentiated Pareto Distribution and its original form. Some structural properties of the proposed distribution are studied including explicit expressions for the moments. We provide the density function of the order statistics and obtain their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. The real data is provided to illustrate the theoretical results in the complete data.
Key Words and Phrases: Hazard function, Kumaraswamy distribution, Moment, Maximum likelihood estimation, Exponentiated Pareto distribution.