%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 }