A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Gumbel's Extreme Value I Distribution: A New Look
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.
Gumbel's Extreme Value I Distribution: A New Look
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.
Gumbel's Extreme Value I Distribution: A New Look
Lettenmaier, Dennis P. (author) / Burges, Stephen J. (author)
Journal of the Hydraulics Division ; 108 ; 502-514
2021-01-01
131982-01-01 pages
Article (Journal)
Electronic Resource
Unknown
Flood Management in Mahanadi Basin using HEC-RAS and Gumbel’s Extreme Value Distribution
| Springer Verlag | 2018
Parameter and Quantile Estimation for the Generalized Extreme-value Distribution: A Second Look
| Online Contents | 1999
Unified Extreme-Value Distribution
| British Library Online Contents | 2017