The generalized exponential (GE) distribution is the well-established
generalization of the exponential distribution in statistical literature.
Tahir et al. (2015) proposed a flexible probability generator called the odd
generalized exponential-G (OGE-G) family of distributions. In this article,
we propose a bivariate extension of the OGE-G class, in the so-called the
bivariate odd generalized exponential-G (BOGE-G) family of distributions,
whose marginal distributions are OGE-G families. Important mathematical and
statistical properties of the BOGE-G family including joint density function
with its marginals, Marshall-Olkin copula, product moments, covariance,
conditional densities, median correlation coefficient, joint reliability
function, joint hazard rate function with its marginal functions, marginal
asymptotic, and distributions for both max(X1,X2) and min(X1,X2), are
derived. After the general class is introduced, a sub-model is discussed in
detail. The maximum likelihood approach is utilized for estimating the
bivariate family parameters. A simulation study is carried out to assess the
performance of the sub-model parameters. A real-life data set is analyzed to
illustrate the flexibility of the proposed bivariate class.