Distribution of the Joint Survival Function of an Archimedean Copula

Suppose a random vector [Formula: see text] with values in the unit cube has a joint survival function: [Formula: see text] given by an Archimedean copula [Formula: see text] with generator [Formula: see text], a smooth decreasing convex function such that [Formula: see text]. In this article, we provide a formula for the distribution of [Formula: see text] where [Formula: see text] is an independent copy of [Formula: see text] and a method to simulate values from the distribution of Z in the bivariate case, that is, when d = 2. The case d > 2 does not seem to be tractable. As an application, we show how our result can be used to compute the limiting covariance of the empirical Kendall process corresponding to [Formula: see text]. AMS Subject Classification: 62H05