The three-parameter generalized extreme-value (GEV) distribution has found wide application for describing annual floods, rainfall, wind speeds, wave heights, snow depths, and other maxima. Previous studies show that small-sample maximum-likelihood estimators (MLE) of parameters are unstable and recommend L moment estimators. More recent research shows that method of moments quantile estimators have for −0.25 < κ < 0.30 smaller root-mean-square error than L moments and MLEs. Examination of the behavior of MLEs in small samples demonstrates that absurd values of the GEV-shape parameter κ can be generated. Use of a Bayesian prior distribution to restrict κ values to a statistically/physically reasonable range in a generalized maximum likelihood (GML) analysis eliminates this problem. In our examples the GML estimator did substantially better than moment and L moment quantile estimators for − 0.4 ≤ κ ≤ 0.
Description
Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data
%0 Journal Article
%1 Martins.Stedinger2000
%A Martins, Eduardo S.
%A Stedinger, Jery R.
%D 2000
%I AGU
%J Water Resour. Res.
%K Bayesian FisherInformation GEV GML HoskingsAlgorithm LMoments Likelihood MOM NewtonRaphson PWeightedMoments PriorGeophysical Simulation Simulation:MonteCarlo asymptotic:efficiency asymptotic:normality censoreddata computation historicaldata prior scoring smallsampleproperties stationary
%N 3
%P 737--744
%R 10.1029/1999WR900330
%T Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data
%U http://dx.doi.org/10.1029/1999WR900330
%V 36
%X The three-parameter generalized extreme-value (GEV) distribution has found wide application for describing annual floods, rainfall, wind speeds, wave heights, snow depths, and other maxima. Previous studies show that small-sample maximum-likelihood estimators (MLE) of parameters are unstable and recommend L moment estimators. More recent research shows that method of moments quantile estimators have for −0.25 < κ < 0.30 smaller root-mean-square error than L moments and MLEs. Examination of the behavior of MLEs in small samples demonstrates that absurd values of the GEV-shape parameter κ can be generated. Use of a Bayesian prior distribution to restrict κ values to a statistically/physically reasonable range in a generalized maximum likelihood (GML) analysis eliminates this problem. In our examples the GML estimator did substantially better than moment and L moment quantile estimators for − 0.4 ≤ κ ≤ 0.
@article{Martins.Stedinger2000,
abstract = {The three-parameter generalized extreme-value (GEV) distribution has found wide application for describing annual floods, rainfall, wind speeds, wave heights, snow depths, and other maxima. Previous studies show that small-sample maximum-likelihood estimators (MLE) of parameters are unstable and recommend L moment estimators. More recent research shows that method of moments quantile estimators have for −0.25 < κ < 0.30 smaller root-mean-square error than L moments and MLEs. Examination of the behavior of MLEs in small samples demonstrates that absurd values of the GEV-shape parameter κ can be generated. Use of a Bayesian prior distribution to restrict κ values to a statistically/physically reasonable range in a generalized maximum likelihood (GML) analysis eliminates this problem. In our examples the GML estimator did substantially better than moment and L moment quantile estimators for − 0.4 ≤ κ ≤ 0.},
added-at = {2010-12-02T12:26:23.000+0100},
author = {Martins, Eduardo S. and Stedinger, Jery R.},
biburl = {https://www.bibsonomy.org/bibtex/20c6b054229c0b1a41b185ee225eb021a/marsianus},
description = {Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data},
doi = {10.1029/1999WR900330},
interhash = {97ea0352960589642b9556af4b70accb},
intrahash = {0c6b054229c0b1a41b185ee225eb021a},
issn = {00431397},
journal = {Water Resour. Res.},
keywords = {Bayesian FisherInformation GEV GML HoskingsAlgorithm LMoments Likelihood MOM NewtonRaphson PWeightedMoments PriorGeophysical Simulation Simulation:MonteCarlo asymptotic:efficiency asymptotic:normality censoreddata computation historicaldata prior scoring smallsampleproperties stationary},
number = 3,
pages = {737--744},
publisher = {AGU},
timestamp = {2013-11-18T15:47:52.000+0100},
title = {Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data},
url = {http://dx.doi.org/10.1029/1999WR900330},
volume = 36,
year = 2000
}