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以及灾难性的自然和人为事件的了解。该项目将建立综合三个概念/问题的数学基础：a)最大可能洪水(PMF)的重现期；b)极端情况的统计和概率分布函数的选择；c)从对应于低频率/高影响事件的分区多目标风险方法(PMRM)得出的条件预期损害。这项工作将增加和改进我们对与极端自然事件相关的随机过程的理解。将开展五项工作，它们是：1)建立关于PMF重现期的先验假设与其对大坝安全问题的影响之间的可信而明确的数学关系；2)将研究结果扩展到PMF重现期的一般动力学；3)将PMRM与极值统计量之间的关系从某些密度扩展到更大的分布类别；4)将极端事件条件期望值的概念与重现期的概念联系起来；5)将任务3和任务4结合起来，建立了设想的数学模型。建议设立小说研究加速奖。

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.