A New Generalization of the Gompertz distribution

‎In this paper‎, ‎a new distribution of the three-parameter lifetime model called the Marshall-Olkin Gompertz is proposed on the basis of the Gompertz distribution‎. ‎It is a generalization of the Gompertz distribution having decreasing failure rate and can also be increasing and bathtub-shaped depending on its parameters‎. ‎The probability density function‎, ‎cumulative distribution function‎, ‎hazard rate function and some mathematical properties of this model such as‎, ‎central moments‎, ‎moments of order statistics‎, ‎Renyi and Shannon entropies and quantile function are derived‎. ‎In addition‎, ‎the maximum likelihood of its parameters method is estimated and this new distribution compared with some Gompertz distribution generalizations by means of a set of real data‎.