{"paper":{"title":"On the penultimate tail behavior of Weibull-type models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Marta Ferreira","submitted_at":"2011-09-14T17:17:59Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3139","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}