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Goodness‐of‐fit tests for regional generalized extreme value flood distributions
Author(s) -
Chowdhury Jahir Uddin,
Stedinger Jery R.,
Lu LiHsiung
Publication year - 1991
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/91wr00077
Subject(s) - statistics , skewness , mathematics , estimator , goodness of fit , monte carlo method , generalized extreme value distribution , kolmogorov–smirnov test , moment (physics) , gamma distribution , statistical hypothesis testing , extreme value theory , physics , classical mechanics
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.