Bivariate extreme-value copulas with discrete Pickands dependence measure
Bivariate extreme-value copulas with discrete Pickands dependence measure
复制标题
具有离散 Pickands 依赖度量的双变量极值联结函数
DOI：
10.1007/s10687-010-0112-8
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发表时间：
2011
期刊：
影响因子：
1.3
通讯作者：
M. Scherer
中科院分区：
文献类型：
--
作者：
Jan;M. Scherer
引入并分析了一类双参数族的二元极值copula (EVCs)，它精确地对应于Pickands依赖测度最多为两个原子的二元极值copcs。给出了具有任意离散Pickands依赖测度的二元evc如何被表示为这种基联的几何平均值。因此，一般的二元evc可以表示为这种结构的极限，当涉及的基联数趋于无穷时。除了这种表示的理论价值外，还说明了如何从所涉及的基联的性质推导出所表示的联的几个性质。给出了一种表示的计算算法。
A two-parametric family of bivariate extreme-value copulas (EVCs), which corresponds to precisely the bivariate EVCs whose Pickands dependence measure is discrete with at most two atoms, is introduced and analyzed. It is shown how bivariate EVCs with arbitrary discrete Pickands dependence measure can be represented as the geometric mean of such basis copulas. General bivariate EVCs can thus be represented as the limit of this construction when the number of involved basis copulas tends to infinity. Besides the theoretical value of such a representation, it is shown how several properties of the represented copula can be deduced from properties of the involved basis copulas. An algorithm for the computation of the representation is given.