  Max-stable processes are widely used to model spatial extremes. These
processes exhibit asymptotic dependence meaning that the large values of the
process can occur simultaneously over space. Recently, inverted max-stable
processes have been proposed as an important new class for spatial extremes
which are in the domain of attraction of a spatially independent max-stable
process but instead they cover the broad class of asymptotic independence. To
study the extreme values of such processes we use the conditioned approach to
multivariate extremes that characterises the limiting distribution of
appropriately normalised random vectors given that at least one of their
components is large. The current statistical methods for the conditioned
approach are based on a canonical parametric family of location and scale
norming functions. We study broad classes of inverted max-stable processes
containing processes linked to the widely studied max-stable models of
Brown-Resnick, Schlather and Smith, and identify conditions for the
normalisations to either belong to the canonical family or not. Despite such
differences at an asymptotic level, we show that at practical levels, the
canonical model can approximate well the true conditional distributions.
