联结(copula)函数在概率地震危险性分析中的应用

The copula joint function and its application in probabilistic seismic hazard analysis

介绍了一种成熟的已广泛应用于金融领域的估计不确定性的方法——copula函数方法,并推广了n重的Frank’s copulas;在实际应用中,本文采用了俞言祥和美国西部由Boore等人给出的两个衰减模型,针对其中存在的模型不确定性以及它们之间的相互依赖性,构造出概率意义上联合的copula分布函数,并将其应用于实例分析.结果表明,对比于传统逻辑树中所用的线性结合方法,copula将两者带来的概率分布写成一个联合概率分布,能够很好地考虑双方不尽相同的意见.另外,由于copula函数可采用各种各样的边际分布函数来获得联合概率分布,且在金融风险投资评估已有大量的应用,因此在现代地震危险性评估中将有着广泛的前景.

This paper introduces a new mature mathematical technique used to deal with models＇ uncertainty in financial risk analysis-copula joint function, and generalize it to the n-dimensional Frank＇s copula. In addition, we used a two-dimensional copula joint probabilistic function as an example to illustrate the uncertainty treatment at low probability tion models derived from Yu and Boore et al level between two different attenua- , and the result shows a better esti- mation than that given by linear weight technique usually used in the traditional logic-tree method. In light of widespread application in the risk analysis in the financial investment and insurance assessment, we believe that the copula-based method will have a potential application in the seismic hazard analysis.