Parameter estimation in a regional flood frequency setting, based on a Weibull model, is revisited. A two parameter Weibull distribution at each site, with common shape parameter over sites that is rationalized by a flood index assumption, and with independence in space and time, is assumed. The estimation 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 estimator and its asymptotic variance for each technique, suggested by trying to minimize the asymptotic variance over the family of estimators, is obtained. These asymptotic variances are compared to the Cramer-Rao Lower Bound, which is known to be the asymptotic variance of the maximum likelihood estimator. A companion paper considers the application of this model and these estimation techniques to a real data set. It includes a simulation study designed to indicate the sample size required for compatibility of the asymptotic results to fixed sample sizes.
Bibliographical noteFunding Information:
The research leading to this paper has been sponsored by the US National Science Foundation Grant CMS-9625685 on “Uncertainty and Risk Analysis under Extreme Hydrologic Events” and Internal Research Fund of Yonsei University, Korea. Acknowledgment is due to two anonymous reviewers who provided important suggestions that improved the paper.
All Science Journal Classification (ASJC) codes
- Water Science and Technology