On a family that unifies Generalized Marshall-Olkin and Poisson-G family of distribution

Abstract: Unifying the generalized Marshall-Olkin (GMO) and Poisson-G (P-G) a new family of distribution is proposed. Density and the survival function are expressed as infinite mixtures of P-G family. The quantile function, asymptotes, shapes, stochastic ordering, moment generating function, order statistics, probability weighted moments and R\'enyi entropy are derived. Maximum likelihood estimation with large sample properties is presented. A Monte Carlo simulation is used to examine the pattern of the bias and the mean square error of the maximum likelihood estimators. An illustration of comparison with some of the important sub models of the family in modeling a real data reveals the utility of the proposed family.