Abstract
To test the extreme value condition, Cramér–Von Mises type tests were recently proposed by Drees et al. (2006) and Dietrich et al. (2002). Hüsler and Li (2006) presented a simulation study on the behavior of these tests and verified that they are not robust for models in the domain of attraction of a max-semistable distribution function. In this work we develop a test statistic that distinguishes quite well distribution functions which belong to a max-stable domain of attraction from those in a max-semistable one. The limit law is deduced and the results from a numerical simulation study are presented.
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