Inferences on the Weibull Exponentiated Exponential Distribution and Applications

Abstract

In this article, an alternative method of defining the probability density function of Generalized Weibull-exponential distributions is proposed. Based on the method, the distribution can also be called Weibull exponentiated exponential distribution. This distribution includes the exponential, Weibull and exponentiated exponential distributions as special cases. Comprehensive mathematical treatment of the distribution is provided. The quantile function, mode, characteristic function, moment generating function among other mathematical properties of the distribution were derived. The parameters of the distribution were estimated by applying the Maximum Likelihood Procedure.The elements of the Fisher Information Matrix is also provided. Finally, a data set is fitted to the model and its sub-models. It is observed that the new distribution is more flexible and can be used quiet effectively in analysing real life data in place of exponential, Weibull and exponentiated exponential distributions.