Efficiently sampling exchangeable Cuadras-Augé copulas in high dimensions

An n-dimensional random vector is constructed whose survival copula is given by a copula that was first presented in Cuadras and Augé [C.M. Cuadras, J. Augé, A continuous general multivariate distribution and its properties, Communications in Statistics - Theory and Methods 10 (4) (1981) 339-353]. This construction adds a Poisson subordinator as mixing variable to initially independent exponentially distributed random variables. It is shown how the choice of Poisson process relates to the parameter of the induced Cuadras-Augé copula. Based on this construction, a sampling algorithm for this multivariate distribution is presented which has average computational efficiency O (n log log n).