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(nloglogn)O(nloglogn).