當(dāng)構(gòu)建多個隨機變量的聯(lián)合分布時，可以分兩步，第一先有每個變量的邊際分布。第二描述這些變量如何related to each other，這個描述就是Copula。精確定義如下
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其實是個多元函數(shù)。Sklar定理保證這種描述方式make sense。因為此多元函數(shù)存在并且在連續(xù)情況下唯一。
兩種常見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.
