VARIANCE OF 2-PARAMETER AND 3-PARAMETER GEV PWM QUANTILE ESTIMATORS - FORMULAS, CONFIDENCE-INTERVALS, AND A COMPARISON

Simple formulae are developed for the sampling variances of quantile estimators for generalized extreme value (GEV) distributions when probability weighted moments (PWM) or L-moments are used to estimate all three parameters, or just two parameters given the GEV shape parameter. Sampling variances of three-parameter 100-year flood estimators can be reduced by a factor of 2-3 if the GEV shape parameter is specified. For distributions with realistic shape parameters, the two-parameter 100-year flood estimator with a fixed regional shape parameter (such as a Gumbel estimator) generally has a smaller m.s.e. than does a three-parameter estimator, even if the shape parameter is misrepresented. On the other hand, for less extreme quantiles with exceedance probabilities greater than 0.10, when kappa less-than-or-equal-to 0.0, the three-parameter quantile estimators generally had smaller m.s.e.