Multivariate extreme value analysis and its relevance in a metallographical application

Motivated from extreme value (EV) analysis for large non-metallic inclusions in engineering steels and a real data set, the benefit of choosing a multivariate EV approach is discussed. An extensive simulation study shows that the common univariate setup may lead to a high proportion of mis-specifications of the true EV distribution, as well as that the statistical analysis is considerably improved when being based on the respective data of <italic>r</italic> largest observations, with <italic>r</italic> appropriately chosen. Results for several underlying distributions and various values of <italic>r</italic> are presented along with effects on estimators for the parameters of the generalized EV family of distributions.