A bivariate probability generator for the odd generalized exponential model: Mathematical structure and data fitting

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.