Author(s): Weiqiang Zheng; Shuguang Liu; Zhengzheng Zhou; Guihui Zhong

Linked Author(s):

Keywords: Interval estimation; Pivotal quantity; Generalized extreme value distribution; Frequency analysis

Abstract: A common approach on extreme value analysis in flood management is using a fitted distribution, usually the generalized extreme value (GEV) distribution, to estimate the design values under a given return period. However, due to the complexity of the hydrological process and the finiteness of observed-data size, the estimated return levels are often expressed by confidence intervals to consider the related uncertainties. Previous studies have shown that conventional bootstrap method sometimes provides over narrow or wide confidence intervals in GEV distribution. Therefore, in this study, we conduct confidence interval estimations for the GEV distribution based on three specially designed pivotal quantities. The distributions of these quantities are determined only by the sample size. The feasibility and reliability of this approach is studied and compared to conventional bootstrap methods. It is found that the proposal pivotal quantity method improves the coverage of confidence intervals for design values compared to nonparametric and parametric bootstrap methods, especially when the sample sizes are small and when the return periods are high. Also, the pivotal quantity method and the parametric bootstrap method have their own advantages in the interval estimations for parameters. The proposal pivotal quantities can also be recommended in other three-parameter extreme-value distributions to yield more reliable interval estimations in flood frequency analysis.

DOI: https://doi.org/10.64697/978-90-835589-7-4_41WC-P1624-cd

Year: 2025