Goodness‐of‐fit tests for regional generalized extreme value flood distributions

Abstract

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.