Multivariate extreme value analysis and its relevance in a metallographical application

Abstract

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 r largest observations, with r appropriately chosen. Results for several underlying distributions and various values of r are presented along with effects on estimators for the parameters of the generalized EV family of distributions.

Extension of ASTM E2283 standard practice for the assessment of large exogenous nonmetallic inclusions in super duty steels

“…For example, the authors [19][20][21] suggested estimating the size of NMIs on the fracture surface of specimens or on each individual inclusion isolated from a metal by electrolytic dissolution. In other works, instead of the Gumbel distribution, the other distributions of extreme values were used: Weibull or Fréchet [22][23][24] and Pareto [25,26]. However, the advantages of such methods and the novelty of the results obtained in these works [19][20][21] do not justify the com- plexity of the methods and do not comply with the current standard [18].…”