The Gauss hypergeometric Gleser distribution with applications to flood peaks exceedance and income data

Abstract

We introduced the Gauss hypergeometric Gleser (GHG) distribution, a novel extension of the Gleser (G) distribution that unifies families of Gleser distributions. We studied their representations and some basic properties and showed that the GHG distribution is heavy-tailed. The maximum likelihood method is used for parameter estimation, and the Fisher information matrix derived. We assessed the performance of the maximum likelihood estimators via Monte Carlo simulations. Moreover, we present applications to two data sets in which the GHG distribution shows a better fit than other known distributions.