Given a bivariate dataset \((X_i, Y_i)_i\) of \(n\) points,
two variables are defined:
(1) for output="orig", the \(\tilde Z_{\omega,i}\) variable
$$\tilde Z_{\omega,i} = \min \left(
f\left(\frac{R_i^X}{n+1}\right),
\frac{\omega}{1-\omega} f\left(\frac{R_i^Y}{n+1}\right) \right)
$$
where \(f(x)\) is the margin transformation and \(i=1,...,n\);
(2) for output="relexcess", the \(Z_{j}\) variable
$$
\frac{\widetilde Z_{\omega,n-m+j,n}}{\widetilde Z_{\omega,n-m,n}}
$$
where \(m\) equals nbpoint, \(j=1,\dots, m\),
and \(\widetilde Z_{\omega,1,n},...,
\widetilde Z_{\omega,n,n}\) are the order statistics of
\(\widetilde Z_{\omega,1},...,\widetilde Z_{\omega,n}\).
The margin transformation is
$$
f(x) = \frac{1}{1-x}, f(x) = \frac{1}{-\log(x)}, f(x) = x,
$$
respectively for unit Pareto (marg="upareto"),
unit Frechet (marg="ufrechet") and unit uniform margin
(marg="uunif").