Regional flood frequency analysis based on a Weibull model

Part 1. Estimation and asymptotic variances

Jun-Haeng Heo, D. C. Boes, J. D. Salas

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)157-170
Number of pages14
JournalJournal of Hydrology
Volume242
Issue number3-4
DOIs
Publication statusPublished - 2001 Feb 28

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flood frequency
frequency analysis
simulation
family
method
parameter
distribution
index
parameter estimation

All Science Journal Classification (ASJC) codes

  • Water Science and Technology

Cite this

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abstract = "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.",
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Regional flood frequency analysis based on a Weibull model : Part 1. Estimation and asymptotic variances. / Heo, Jun-Haeng; Boes, D. C.; Salas, J. D.

In: Journal of Hydrology, Vol. 242, No. 3-4, 28.02.2001, p. 157-170.

Research output: Contribution to journalArticle

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