The Marshall-Olkin Extended Weibull-Exponential Distribution: Properties and Applications

Abstract

In this paper, a new probability distribution is introduced following the work of Marshall and Olkin [1]. Sub models of the proposed distribution are also important models used in the literature. Expressions for some of its properties such as limiting behavior, quantile function, moments, moment generating function, order statistics, entropy, and reliability functions are derived. The method of maximum likelihood is used in the estimation of the model parameters. The graphs of the hazard rate function plotted for some values of the parameters show that the distribution can be used to model data which exhibits decreasing, increasing or bathtub hazard rate behavior. Series expression of the probability density function was also obtained which enables the expression of some properties of the new distribution in terms of the properties of the base distribution. The distribution is fitted to two real life datasets to show its flexibility and usefulness. Its goodness-of-fit indices indicate better fit to the datasets than the three other distributions compared with it. Contribution/ Originality: This study originates a new probability distribution named Marshall-Olkin Extended Weibull-Exponential distribution (MOEWED) which is a four-parameter continuous univariate probability distribution capable of modelling data sets of diverse shapes of distribution including approximately symmetric, left-skewed, right-skewed, J-shape, reversed J-shape and unimodal shapes.