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www.hydrol-earth-syst-sci.net/8/1174/2004/
doi:10.5194/hess-8-1174-2004
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The construction of confidence intervals for frequency analysis using resampling techniques: a supplementary note
1WL|Delft Hydraulics, PO Box 177, 2600 MH Delft, The Netherlands
2UNESCO-IHE Institute for Water Education, PO Box 3015, 2601 DA Delft, The Netherlands
Email for corresponding author: m.hall@unesco-ihe.org
Abstract. In a recent contribution, Hall et al. (2004) examined the use of the Bootstrap resampling technique as a means of constructing confidence limits for the quantiles of the (two-parameter) Gumbel and the (three-parameter) Weibull distributions. Particular emphasis was placed on the behaviour of sample sizes of the order of 30, which are typical of those encountered in hydrological frequency analysis. The resampled confidence limits obtained for the Gumbel distribution were found to be comparable with those based upon a well-known theoretical approximation. However, those for samples of size 30 from the Weibull distribution were shown to be more problematical, with the results dependent upon the skewnesses of the resampled distributional parameters. For a further and more quantitative assessment of the suitability of Bootstrap resampling for constructing confidence intervals, so-called coverage rates were evaluated for the Weibull distribution in a supplementary study. The results show a satisfactory performance when using the percentile method but do not really mitigate the conclusion of the original study that resampled confidence limits should be employed with caution when sample sizes are of the order of 30.
Keywords: Bootstrap, Jack-knife, frequency analysis, maximum likelihood method, maximum product of spacings method, confidence intervals, coverage rates
Final Revised Paper (PDF, 566 KB)
Citation: van den Boogaard, H. F. P. and Hall, M. J.: The construction of confidence intervals for frequency analysis using resampling techniques: a supplementary note, Hydrol. Earth Syst. Sci., 8, 1174-1178, doi:10.5194/hess-8-1174-2004, 2004. Bibtex EndNote Reference Manager XML
