On the penultimate tail behavior of Weibull-type models

Details On the penultimate tail behavior of Weibull-type models On the penultimate tail behavior of Weibull-type models

2011-09-14

arxiv.org/abs/1109.3139v2

Mathematics

Statistics Theory

Scientific paper

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.

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