配备FGM Copulas二维随机向量之和的相依性

本文研究了配备Farlie-Gumbel-Morgenstern Copulas的二维随机向量之和的相依性,得到了在这类Copulas函数下两个独立的随机向量之和的Kendall及Spearman相依系数的一般公式;并针对边缘分布分别为指数分布的情况推导出了具体的公式;证明了当边缘分布满足一定的条件时,不存在尾部相依性.此外,对于几种不同边缘分布的情况进行了随机模拟与比较.这些方法及结果对两个企业(公司)合并后某两个随机指标之间的相依性问题的研究具有理论指导意义,为这类问题的进一步探索提供了理论基础.

Dependence on Sum of Bivariate Random Vectors with FGM Copulas

The dependence on the sum of bivariate random vectors with Farlie-Gumbel-Morgenstern copulas is studied in the paper. Firstly, the Kendall's  and the Spearman's  on two independent random vectors' sum with the copulas are deduced, and the specific equation with exponential marginal distribution is shown. Then, the proposition is proved that there exists no tail-dependence under some conditions on marginal distribution. Finally, we calculate some numerical instances for different marginal distributions by using Monte Carlo method. The conclusions and methods in this paper have theoretical significance for the dependence between two random indices of the combination of enterprise, and lay foundations for the further study.