English

On the penultimate tail behavior of Weibull-type models

Statistics Theory 2011-09-27 v2 Statistics Theory

Abstract

The Gumbel max-domain of attraction corresponds to a null tail index which do not distinguish the different tail weights that might exist between distributions within this class. The Weibull-type distributions form an important subgroup of this latter and includes the so-called \emph{Weibull-tail coefficient}, usually denoted \theta, that specifies the tail behavior, with larger values indicating slower tail decay. Here we shall see that the Weibull-type distributions present a penultimate tail behavior Fr\'echet if \theta>1 and a penultimate tail behavior Weibull whenever \theta<1.

Keywords

Cite

@article{arxiv.1109.3139,
  title  = {On the penultimate tail behavior of Weibull-type models},
  author = {Marta Ferreira},
  journal= {arXiv preprint arXiv:1109.3139},
  year   = {2011}
}
R2 v1 2026-06-21T19:04:49.433Z