Multivariate Compound Extreme Value Distribution and Its Application
Multivariate Compound Extreme Value Distribution and Its Application
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发表时间：
2004
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通讯作者：
Wang Li
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作者：
Wang Li
随着海洋工程的发展，极端海洋环境下的联合概率问题越来越受到数学家和工程师的关注。然而，传统的多变量概率分布模型不能描述台风、飓风或冬季风暴引起的极端海况的分布，不能全面反映海洋环境的概率特征。极端的海洋环境通常出现在台风等风暴中，在某些海域，这种风暴的发生每年都有变化，可以拟合成离散分布。本文将离散分布与某些极端海洋环境的多元连续分布复合，得到一种新的分布--多元复合极值分布（MCEVD）。Poisson套Logistic三变量复合极值分布和Poisson-Gumbel混合复合极值分布，本文的第二部分提出了MCEVD的随机模拟技术。理论解和随机模拟技术已用于上海市防灾设计水位预报、香港海域防波堤平台净空越浪设计和长江洪水（峰、量、频）分析。
With the development of offshore engineering, the joint probability study for extreme sea environments has been a subject of increasing interest to both mathematicians and engineers. However, the conventional multivariate probability distribution models do not describe the distribution of the occurrences of extreme sea states induced by Typhoon, Hurricane or winter storm, and thus fail to reflect the probability characteristics of sea environments in all their aspects. Extreme sea environments are typically to be found in storms like Typhoon, and the occurrences of such storms in certain sea areas, varying from year to year, may be fitted to a discrete distribution. By compounding the discrete distribution with a multivariate continuous distribution of some extreme sea environments, a new kind of distribution—Multivariate Compound Extreme Value Distribution(MCEVD) is obtained in this paper.The first part of this paper proposes two types of MCEVD: Poisson-Nested Logistic Trivariate Compound Extreme Distribution and Poisson-Gumbel Mixed Compound Extreme Distribution.The second part of this paper proposes the stochastic simulation technique for MCEVD. Both the theoretical solutions and stochastic simulation techniques are used in predicting disaster prevention design water level for Shanghai city, in designing of platform deck clearance wave overtopping of breakwaters in the Hong-Kong sea areas, and in flood(peak, voluame, frequency) analysis fo the Yangze River.