Extreme value theory in mixture distributions and a statistical method to control the possible bias

Wonseon Gwak, Hyein Goo, Yang Ho Choi, Jae Youn Ahn

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper, extreme behaviors of a mixture distribution are analyzed. We investigate some cases where the mixture distributions are in the proper domain of attraction so that the extreme value of mixture distributions converges to the proper Generalized Extreme Value distribution (GEV). However, in general, there is no guarantee that the distribution of the data is in the proper maximum domain of attraction. Furthermore, since the convergence rate can be slow even with guaranteed asymptotic convergence, GEV estimation method might provide a biased estimation, as shown in Choi et al. (2014). The paper provides a safe method to control the quality of the quantile estimator in extreme values.

Original languageEnglish
Pages (from-to)581-594
Number of pages14
JournalJournal of the Korean Statistical Society
Volume45
Issue number4
DOIs
StatePublished - 1 Dec 2016

Keywords

  • Extreme behavior
  • Generalized Extreme distribution
  • Mixture distribution
  • Precipitation

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