Copula

A generalised representation of the dependence between a set of random variables \(X_i\) given by the joint cumulative distribution function \(C\) of a set of dependent standard uniform random variables \(U_i\)
\[ C\left(u_0, u_1, \dots\right) = \Pr\left(U_0 \leqslant u_0 \wedge U_1 \leqslant u_1 \wedge \dots\right) \]
where \(\wedge\) means and, such that if those random variables have a joint CDF of \(H\) and CDFs of \(F_i\) when observed independently then
\[ H\left(x_0, x_1, \dots\right) = C\left(F_0\left(x_0\right), F_1\left(x_1\right), \dots\right) \]