This paper develops critical values and formulas for computing several goodness-of-fit tests for the generalized extreme value (GEV) distribution. These tests can check if data available for a site are consistent with a regional GEV distribution, except for scale, or if the data are consistent with a GEV distribution with a regional value of the shape parameter κ. Three tests employ unbiased probability-weighted moment (PWM) estimators of the L moment coefficient of variation (L-CV), and coefficient of skewness (L-CS) using formulas for their variances in small samples. In a Monte Carlo power study the L-CV test was often more powerful than the Kolmogorov-Smirnov test at detecting L-CV inconsistencies. A test based upon L-CS generally has equal or greater power than the probability plot correlation test at detecting L-CS differences; both are poor at detecting thin-tailed alternatives. Finally, a new chi-square test based upon sample estimates of both the L-CV and L-CS, and their anticipated cross correlation, was much better than other tests at detecting departures from the assumed L-CV, L-CS, or both, particularly when the regional distribution was highly skewed.
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