Exponentiated modified Weibull extension distribution

A new modified Weibull extension distribution is proposed by Xie et al. [20]. Recently, El‐Gohary et al. [9] proposed a new distribution referred to as the generalized Gompertz distribution. In this paper, we propose a new model of a life time distribution that mainly generalizes these two distributions. We refer to this new distribution as the exponentiated modified Weibull extension distribution. This distribution generalizes, in addition to the above two mentioned distributions, the exponentiated Weibull distribution, the generalized exponential and the generalized Rayleigh distributions. Parameter estimation of the four parameters of this distribution is studied. Two real data sets are analyzed using the new distribution, which show that the exponentiated modified Weibull extension distribution can be used quite effectively in fitting and analyzing real lifetime data.