the order statistics below the within-block maximum. Further, ML estimation needs to evaluate the multivariate densities while for many max-stable models only the bivariate densities are known in closed form. Thus, composite likelihood approaches have been proposed [@pad2010; @dav2012].\
In univariate extreme-value theory, the second standard procedure estimates parameters by fitting a certain PPP to the *peaks-over-thresholds* (POT), i.e., to the empirical process of exceedances over a certain critical value [@lea1991; @emb1997]. Also in the multivariate framework we can expect to profit from using all extremal data via generalized POT methods instead of aggregated data. In contrast to the ML approach, in this paper, we assume that $\xi$ admits one of the two representations and and we aim at extracting realizations of the processes $W$ and $F$, respectively, from *single extreme events*. Here, the specification of a single extreme event will depend on the respective representation.\
In [@eng2012a], this concept is applied to derive estimators for the class of Brown-Resnick processes [@bro1977; @kab2009], which have the form by construction. With $a(n)$ being a sequence of positive numbers with $\lim_{n\to\infty} a(n) = \infty$, the convergence in distribution $$\begin{aligned}
    \Bigg( \frac{\eta(t_1)}{\eta(t_0)}, \ldots, 
    \frac{\eta(t_k)}{\eta(t_0)} 
    \ \Bigg|\ 
    \eta(t_0) > a(n) \Bigg)\cvgdist \bigl(
    W(t_1),\dots, W(t_k) 