Integration of the Statistics of Extremes, the Conditional Expectation and the Probable Maximum Flood

这项工作的目的是加强对风险和灾难性自然和人为事件的理解。该项目将发展数学基础，其中将整合三个概念/问题：a)最大可能洪水的重现期（PMF）；B)统计极值和概率分布函数的选择；c)由分区多目标风险法（PMRM）得出的对应于低频率/高冲击事件的条件预期损害。这项工作将增加和改善我们对与极端自然事件相关的随机过程的理解。本文将开展以下五项工作：1)在PMF回归期的先验假设与其对大坝安全问题的影响之间建立有说服力和明确的数学关系；2)将研究结果扩展到一般PMF回归期的动态；3)将PMRM与极值统计量的关系从一定密度扩展到更大的分布类别；4)将极端事件条件期望概念与回归期概念联系起来；5)整合任务3和任务4，从而创建预想的数学模型。这里推荐一项针对新颖研究的加速奖。

The objective of this work is to enhance the understanding of the risks and catastrophic natural and manmade events. The project will develop the mathematical bases where three concepts/issues will be integrated: a) the return period of the maximum probable flood (PMF); b) the statistics of the extreme and the choice of probability distribution function; and c) the conditional expected damage as derived from the partitioned multiobjective risk method (PMRM) that corresponds to low frequency/high impact events. This work will increase and improve our understanding of the stochastic processes associated with extreme natural events. Five tasks will be carried out, and they are: 1) develop a cogent and definite mathematical relationship between the a-priori assumptions on the return period of the PMF and their effects on dam safety problems; 2) expand findings to the dynamics of the return period of PMF in general; 3) broaden the relationship between PMRM and the statistics of extremes from certain densities to a larger class of distributions; 4) link the concept of conditional expectation of extreme events to the concept of return period; and 5) integrate tasks 3 and 4, so as to create the envisioned mathematical model. An Expedited Award for Novel research is here recommended.