Gumbel-Weibull Distribution: Properties and Applications

Abstract

Some properties of the Gumbel-Weibull distribution including the mean deviations and modes are studied. A detailed discussion of regions of unimodality and bimodality is given. The method of maximum likelihood is proposed for estimating the distribution parameters and a simulation is conducted to study the performance of the method. Three tests are given for testing the significance of a distribution parameter. The applications of Gumbel-Weibull distribution are emphasized. Five data sets are used to illustrate the flexibility of the distribution in fitting unimodal and bimodal data sets.