Empirical Copulas

EmpiricalCopula{d,MT}

Fields:

• u::MT - the matrix of observations.

Constructor

EmpiricalCopula(u;pseudos=true)

The EmpiricalCopula in dimension $d$ is parameterized by a pseudo-data matrix which should have shape (d,N). Its expression is given as :

\[C(\mathbf x) = \frac{1}{N}\sum_{i=1}^n \mathbf 1_{\mathbf u_i \le \mathbf x}\]

This function is very practical, be be aware that this is not a true copula (since $\mathbf u$ are only pseudo-observations). The constructor allows you to pass dirctly pseudo-observations (the default) or will compute them for you. You can then compute the cdf of the copula, and sample it through the standard interface.

References:

• [3] Nelsen, Roger B. An introduction to copulas. Springer, 2006.