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Multivariate environmental contours using C-vine copulas

机译：使用C-vine copulas的多元环境轮廓

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摘要

Characterization of some natural hazards requires modeling the joint probability distribution of several random environmental variables. For instance, extreme sea states may be defined in terms of wave height, peak spectral period, wind velocity, current velocity, and wave direction. Building environmental contours of extreme sea-states thus requires the multivariate probability distribution of such variables. The approach based on vine copulas is a way to construct multivariate distributions using bivariate copulas as building blocks. C-vines are particularly appealing for sets of random variables where one of them is considered to be the key one in governing dependence with the other variables. In this work we present a procedure to build multidimensional environmental contours using C-vines. The formulation for the decomposition of multivariate distributions into bivariate copulas and the estimation of parameters for C-vines is discussed. The procedure is illustrated with an example of trivariate environmental contours. It is then applied to build trivariate environmental contours of significant wave height, peak spectral period and wind velocity using storm hindcast data from the Gulf of Mexico. Implications on considerations for customary design criteria are discussed. Comparisons of the environmental contours using C-vines with those obtained from standard multivariate copulas are also discussed. (C) 2016 Elsevier Ltd. All rights reserved.
机译：一些自然灾害的表征需要对几个随机环境变量的联合概率分布进行建模。例如，可以根据波高，峰值频谱周期，风速，海流速度和波向来定义极端海况。因此，建立极端海洋状态的环境轮廓需要这些变量的多元概率分布。基于藤蔓copulas的方法是一种以双变量copulas为基础构建多元分布的方法。 C-vine对于一组随机变量特别有吸引力，其中一组随机变量被认为是控制与其他变量的依存关系的关键。在这项工作中，我们提出了使用C-vines建立多维环境轮廓的过程。讨论了将多元分布分解为双变量copula的公式以及C型葡萄树的参数估计。以三变量环境轮廓为例说明了该过程。然后使用来自墨西哥湾的风暴后预报数据，将其用于构建具有显着波高，峰值频谱周期和风速的三变量环境等高线。讨论了有关常规设计标准的考虑因素。还讨论了使用C型藤蔓与从标准多变量copulas获得的环境轮廓的比较。 （C）2016 Elsevier Ltd.保留所有权利。

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