Extreme value modelling applied in hydrology

在设计防洪设施或估计洪水损害时，决策往往是基于对河流流量的短暂测量。选择一个统计频率分布来拟合测量值，然后使用拟合的分布来估计未来的洪水。有许多方法可以将分布拟合到数据中。一些分布有一个有限的上界，这是分布参数（形状、规模等）的函数。某些分布拟合方法可能产生与观测数据不一致的上界估计值。当一个或多个样本观测值超过估计分布的上界时，就会发生这种情况。这使得估计的上界不现实。我们将研究一些估计方法与观测数据的不一致，并检查其工程风险后果。我们希望为水文风险分析的统计分布和拟合方法之间的选择建立改进的指导方针。

In designing flood-control structures, or in estimating flood damage, decisions are often made on the basis of a short sample of river flow measurements. A statistical frequency distribution is chosen to fit the measurements, and the fitted distribution is then used to estimate future floods. Many methods exist to fit distributions to data. Some of the distributions have a finite upper bound that is a function of the distribution parameters (shape, scale, etc.). Some distribution fitting methods may produce an estimate of this upper bound that is inconsistent with the observed data. This occurs when one or more sample observations exceed the upper bound of the estimated distribution. This makes the estimated upper bound unrealistic. We will investigate this inconsistency of some estimation methods with the observed data and examine its engineering risk consequences. We hope to establish improved guidelines for choosing between statistical distributions and fitting methods for hydrological risk analysis.