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

Abstract

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.