Bivariate Student distributions with variable marginal degrees of freedom and independence

We propose a class of bivariate Student t distributions generalizing the standard density. Our generalization allows for differing marginal degrees of freedom and independent marginals. There are several approaches to constructing such distributions, but in the special case of the Student-normal distribution we show that there is a common canonical limit. Our distributions arise from the techniques used in t-copula simulation, rather than the traditional elliptical methodology.