Testing whether the shape parameter is zero in the generalized extreme-value distribution

SUMMARY When a sequence of extreme values of a physical process has been observed it is often of interest to test whether the observations are distributed according to a type I Fisher-Tippett extreme-value distribution rather than one of types II or III. This is equivalent to testing whether the shape parameter is zero in the generalized extreme-value distribution. Thirteen tests of this hypothesis are here compared in terms of their empirical significance levels and power in small samples. A modified likelihood ratio test is found to give the best overall performance, and a test due to van Montfort & Otten is also recommended.