Authors: Ahmed M.T. Abd El-Bar; I.E. Ragab
Addresses: Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt ' Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
Abstract: 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.
Keywords: Weibull distribution; WE; hazard rate function; mean residual life function; maximum likelihood estimation; MLE; information matrix.
International Journal of Computing Science and Mathematics, 2018 Vol.9 No.4, pp.309 - 326
Received: 15 Jan 2017
Accepted: 16 Jun 2017
Published online: 11 Sep 2018 *