Research Article
Apr 1982
Gumbel's Extreme Value I Distribution: A New Look
Publication: Journal of the Hydraulics Division
Volume 108, Issue 4
Abstract
Many basic hydrologic textbooks, following Gumbel's original work, advocate use of frequency factors dependent on an integer m for estimation of event levels using the Extreme Value I distribution. Although Gumbel recommended use of m = n, the sample size, it is shown that this choice results in poor estimates, which are much improved by use of m = ∞. This is equivalent to use of the population values. Thus, use of m-dependent tables of frequency factors is misleading and should be avoided. It is also shown that a biased variance estimate (n divisor) yields slightly better estimates of extremes, both in terms of variability and bias, than does the unbiased (n-1 divisor) estimate usually advocated. Finally, modest improvements in estimates, most significant for large return periods and small sample sample sizes, are shown to result from use of maximum likelihood parameter estimators in favor of the best moment estimators.
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Published In
Journal of the Hydraulics Division
Volume 108 • Issue 4 • April 1982
Pages: 502 - 514
Copyright
© 1982 American Society of Civil Engineers.
History
Published in print: Apr 1982
Published online: Feb 3, 2021
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Authors
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Dennis P. Lettenmaier, AM.ASCE
Research Assoc. Prof., Dept. of Civ. Engrg., Univ. of Washington, Seattle, Wash. 98195
Stephen J. Burges, M.ASCE
Prof., Dept. of Civ. Engrg., Univ. of Washington, Seattle, Wash. 98195
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