Before revision:  We provide a convenient and tractable sufficient condition for performing IPA , which is intricate to obtain because of the very structure of max-stable fields involving pointwise maxima over an infinite number of random functions. IPA enables the consistent estimation of the considered measures' derivatives with respect to the parameters characterizing the spatial dependence. We carry out a simulation study which shows that the approach performs well in various configurations  .
After revision:  We provide a convenient and tractable sufficient condition for performing IPA , which is intricate to obtain because of the very structure of max-stable fields . Then we focus on risk and dependence measures, which constitute one of the several frameworks where our theoretical results can be useful. We perform a simulation study which shows that the approach performs well in various configurations .