Multivariate families of gamma-generated distributions with finite or infinite support above or below the diagonal

In this paper, we introduce two new families of multivariate distributions with finite or infinite support above or below the diagonal generated by McKay's bivariate gamma distribution and show that their conditional distributions are univariate gamma- and beta-generated distributions. We derive the Shannon entropies of the introduced families of bivariate distributions. We then focus on the special cases of bivariate gamma-exponentiated exponential distributions, and discuss their properties. Finally, we illustrate the usefulness of the proposed bivariate gamma-exponentiated exponential distributions with a real dataset.