eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2020-01-19 8 1 9 20 10.12691/ajams-8-1-2 AJAMS2020812 article Elebe E. Nwezza emma_nwezza@yahoo.com 1 Chinonyerem V. Ogbuehi 2 Uchenna U. Uwadi 2 C.O. Omekara 2 Department of Mathematics/Computer Science/Statistics/Informatics, Alex Ekwueme Federal University Ndufu alike, Ikwo, Nigeria Department of Statistics, Micheal Okpara University of Agriculture, Umudike, Nigeria In this paper, we propose a new class of Gumbel generated distributions called Gumbel-Marshall-Olkin family of distributions. The new family of distributions is represented as linear mixture of exponentiated-G distribution. Some of the sub-models are presented. We derived some characterizations such as the quantile, moments, moment generating function, entropy and order statistics of the proposed family of distributions. The estimation of the unknown parameters of the new class of distribution is through the maximum likelihood. The consistency of the MLEs of the sub-model is assessed by means of simulation. Furthermore, we derive the bivariate density function of the new class of distributions. Two real life data sets are used to illustrate the potential usefulness of the sub-models of the proposed class of distributions. The results of the applications clearly indicate that the sub-models of the proposed class of distribution provided better fit among the other competing models. http://pubs.sciepub.com/ajams/8/1/2/ajams-8-1-2.pdf Gumbel distribution Marshall-Olkin distribution Bivariate distribution Moment Maximum Likelihood