A New Extended Kumaraswamy Generalized Pareto Distribution With Rainfall Application

Abstract

In this paper, we introduce a new form of Generalized Pareto (GP) distribution which is an extension of Kumaraswamy generalized Pareto (KumGP) distribution based on KM transformation, referred to as KMKGP distribution. The new distribution uncovers more flexibility for data fitting. The maximum likelihood estimation of all parameters and return levels of KMKGP distribution, as well as their confidence intervals, are illustrated. Due to the complexity of likelihood functions, Newton–Raphson procedure is then implemented via simulation study to find the estimated values of all parameters. For goodness-of-fit test, the proposed distribution is also compared to other distributions through actual datasets. The result reveals that KMKGP distribution indicates improvement over other distributions.

Keywords

• Extreme value theory
• generalized Pareto distribution
• Kumaraswamy generalized Pareto distribution
• Kumaraswamy-G class
• KM transformation