Before revision:  In this paper, we consider an underlying model which is popular in spatial extremes , the Smith max-stable random field.
After revision:  In this paper, we consider an underlying model which is popular in spatial extremes . We focus on the two most popular unbiased stochastic derivative estimation approaches: the likelihood ratio method (LRM) and the infinitesimal perturbation analysis (IPA). LRM requires the multivariate density of the max-stable random field.