On a family that unifies the generalized Marshall-Olkin and Poisson-G family of distributions

The aim of the article is to propose a unification of the generalized Marshall-Olkin (GMO) and Poisson-G (P-G) distributions into a new family of distributions. The density and survival function are expressed as infinite mixtures of an exponentiated-P-G family. The quantile function, asymptotes, shapes, stochastic ordering and Rényi entropy are derived. The paper presents a maximum likelihood estimation with large sample properties. A Monte Carlo simulation is used to examine the pattern of the bias and the mean square error of the maximum likelihood estimators. The utility of the proposed family is illustrated through its comparison with some important models and sub models of the family in terms of modeling real data.