A generalisation of the exponential distribution and its applications on modelling skewed data

In this paper, a generalisation of the exponential distribution, namely, Weibull exponentiated-exponential (WEE) distribution, is proposed. The shapes of the density function possess great flexibility. It can accommodate various hazard shapes such as reversed-J, increasing, decreasing, constant and upside-down bathtub. Various properties of the WEE distribution are studied including shape properties, quantile function, expressions for the moments and incomplete moments, probability weighted moments and Shannon entropy. We obtain the asymptotic distributions for the sample minimum and maximum. The model parameters are estimated by maximum likelihood. The usefulness of the new model is illustrated by means of two real lifetime data sets.