  In this paper we study two important representations for extreme value
distributions and their max-domains of attraction (MDA), namely von Mises
representation (vMR) and variation representation (VR), which are convenient
ways to gain limit results. Both VR and vMR are defined via so-called auxiliary
functions psi. Up to now, however, the set of valid auxiliary functions for vMR
has neither been characterized completely nor separated from those for VR. We
contribute to the current literature by introducing ''universal'' auxiliary
functions which are valid for both VR and vMR representations for the entire
MDA distribution families. Then we identify exactly the sets of valid auxiliary
functions for both VR and vMR. Moreover, we propose a method for finding
appropriate auxiliary functions with analytically simple structure and provide
them for several important distributions.
