Jan 9: Copula and Sklar Theorem
2017-01-10 本文已影响0人
茱菁蔓
当构建多个随机变量的联合分布时，可以分两步，第一先有每个变量的边际分布。第二描述这些变量如何related to each other，这个描述就是Copula。精确定义如下
A copula is the joint distribution of random variables U1, U2, . . . ,Up, each of which is marginally uniformly distributed as U(0, 1).
所以Copula其实是个多元函数。Sklar定理保证这种描述方式make sense。因为此多元函数存在并且在连续情况下唯一。
两种常见Copula：Gaussian Copula和t-Copula。
When R = I, the multivariate normal distribution is that of independent standard normal variables, and the copula has a constant density. But the t-copula still shows dependence.
Tail Dependence, which is important in risk management, is coming tomorrow.
