Regional flood frequency analysis based on a Weibull model: Part 2. Simulations and applications

Regional flood frequency analysis based on an index flood assumption and a two-parameter Weibull distribution was studied and simulation experiments were performed to compare the sample properties of quantile estimates based on the maximum likelihood (ML), moments (MOM), and probability weighted moments (PWM) methods, and to determine the applicability of the asymptotic variances of quantile estimators obtained for each method for finite samples. Results of these experiments showed biases and mean square errors vary with sample size, number of sites, nonexceedance probability, shape parameter, and estimation method. The ratio of the asymptotic variance (Avar) and the mean square error has been examined to see how well Avar represents the variability of quantile estimators for finite samples. In general, asymptotic formulas are quite good even for samples of size 25. The proposed regional model and estimation procedures are illustrated by analyzing some actual flood data from Illinois and Wisconsin.