Gumbel's Extreme Value I Distribution: A New Look

by Dennis P. Lettenmaier, (A.M.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,

Serial Information: Journal of the Hydraulics Division, 1982, Vol. 108, Issue 4, Pg. 502-514

Document Type: Journal Paper


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.

Subject Headings: Hydrology | Frequency distribution | Parameters (statistics) | Moment distribution

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