A new three-parameter lifetime distribution

In this paper we introduce a three-parameter distribution called the Weibull exponential (WE) distribution which offers a more flexible model for lifetime data. We show that the hazard rate of the new model can be increasing, decreasing and bathtub shaped. A comprehensive mathematical treatment of the WE distribution is provided. We give closed-form expressions for the density, hazard rate, moments, quantile function, mean residual life function, mean deviations, Bonferroni and Lorenz curves. We also derive the density of order statistic. Moreover, we discuss estimation by the maximum likelihood and obtain an expression for the observed information matrix. Furthermore, simulation results on maximum likelihood estimation are presented. Two real data sets are used to assess the performance of the new model among some classical distributions.