Bivariate Gamma Random Vectors

A seven-parameter family of bivariate probability distributions is developed which allows for any gamma marginal distributions, any associated correlation (positive or negative), and a range of regression curves. The form of the family, which relies on the reproducibility property of the gamma distribution, is motivated by the search for tractable parameter estimation, general dependency structure, and straightforward computer sampling for simulation modeling. A modification with closed-form parameter estimation, but less general dependency structure, is also given. Finally, the use of these distributions in the form of first order autoregressive time series is discussed.