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Multivariate extreme value analysis and its relevance in a metallographical application

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  • A.B. Schmiedt
  • H.H. Dickert
  • W. Bleck
  • U. Kamps

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.

Suggested Citation

  • A.B. Schmiedt & H.H. Dickert & W. Bleck & U. Kamps, 2014. "Multivariate extreme value analysis and its relevance in a metallographical application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 582-595, March.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:3:p:582-595
    DOI: 10.1080/02664763.2013.845872
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    References listed on IDEAS

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    1. Rinya Takahashi & Masaaki Sibuya, 2002. "Metal fatigue, Wicksell transform and extreme values," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 18(3), pages 301-312, July.
    2. Michael E. Robinson & Jonathan A. Tawn, 1995. "Statistics for Exceptional Athletics Records," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 499-511, December.
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