Exponentiated Weibull distribution based on the Marshall-Olkin method

Abstract

This paper proposes the Marshall-Olkin Exponentiated Weibull distribution (MOEW), a new distribution by adding an additional shape parameter to the current Exponentiated Weibull distribution. The goal is to increase the flexibility of the existing Exponentiated Weibull distribution by including an extra shape parameter, resulting in a more flexible distribution that can provide a better fit to various data sets than the baseline distribution. A generator method introduced by Marshall and Olkin is used to develop the new distribution. Some properties of the new distribution such as hazard rate function, survival function, reversed hazard rate function, cumulative hazard function, odds function, quantile function, moments and order statistics are derived. The method of maximum likelihood estimation is used to derive the parameters of the specified model. Monte Carlo simulation is used to evaluate the behavior of the estimators through the average bias and the root mean squared error. The new distribution is fitted and compared with some existing distributions such as the Marshall-Olkin Weibull (MOW), Exponentiated Weibull (EW) and Weibull distributions, on two data sets, namely Breaking stress of carbon fibers (in GPa) and analgesic data sets. Based on the goodness-of-fit statistics and information criteria values, it is demonstrated that the new distribution provides a better fit for the two data sets than the other distributions considered in the study.