Regional flood frequency analysis based on a Weibull model: Part 1. Estimation and asymptotic variances

Parameter estimation in a regional flood frequency setting, based on a Weib ull model, is revisited. A two parameter Weibull distribution at each site, with common shape parameter over sites that is rationalized by a flood ind ex assumption, and with independence in space and time, is assumed. The est imation techniques of method of moments and method of probability weighted moments are studied by proposing a family of estimators for each technique and deriving the asymptotic variance of each estimator. Then a single estim ator and its asymptotic variance for each technique, suggested by trying to minimize the asymptotic variance over the family of estimators, is obtaine d. These asymptotic variances are compared to the Cramer-Rao Lower Bound, w hich is known to be the asymptotic variance of the maximum likelihood estim ator. A companion paper considers the application of this model and these e stimation techniques to a real data set. It includes a simulation study des igned to indicate the sample size required for compatibility of the asympto tic results to fixed sample sizes. (C) 2001 Elsevier Science B.V. All right s reserved.