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Extremes

, Volume 22, Issue 4, pp 667–704 | Cite as

Estimation of extremes for Weibull-tail distributions in the presence of random censoring

  • Julien Worms
  • Rym WormsEmail author
Article
  • 37 Downloads

Abstract

The Weibull-tail class of distributions is a sub-class of the Gumbel extreme domain of attraction, and it has caught the attention of a number of researchers in the last decade, particularly concerning the estimation of the so-called Weibull-tail coefficient. In this paper, we propose an estimator of this Weibull-tail coefficient when the Weibull-tail distribution of interest is censored from the right by another Weibull-tail distribution: to the best of our knowledge, this is the first one proposed in this context. A corresponding estimator of extreme quantiles is also proposed. In both mild censoring and heavy censoring (in the tail) settings, asymptotic normality of these estimators is proved, and their finite sample behavior is presented via some simulations.

Keywords

Weibull-tail Tail inference Random censoring Asymptotic representation 

Mathematics Subject Classification (2010)

Primary 62G32 Secondary 62N02 

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References

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Université Paris-Saclay/Université de Versailles-Saint-Quentin-En-Yvelines, Laboratoire de Mathématiques de Versailles (CNRS UMR 8100)Versailles CedexFrance
  2. 2.Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées (CNRS UMR 8050), UPECCréteilFrance

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