On the penultimate tail behavior of Weibull-type models

2011/09/14 by Ferreira, Marta
#60G70 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1109.3139

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 Weibull-tail coefficient, usually denoted θ, 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 Fréchet if θ>1 and a penultimate tail behavior Weibull whenever θ<1.

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