A New Generalization of the Gompertz distribution

ýIn this paperý, ýa new distribution of the three-parameter lifetime model called the Marshall-Olkin Gompertz is proposed on the basis of the Gompertz distributioný. ýIt is a generalization of the Gompertz distribution having decreasing failure rate and can also be increasing and bathtub-shaped depending on its parametersý. ýThe probability density functioný, ýcumulative distribution functioný, ýhazard rate function and some mathematical properties of this model such asý, ýcentral momentsý, ýmoments of order statisticsý, ýRenyi and Shannon entropies and quantile function are derivedý. ýIn additioný, ýthe 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 dataý.