A Note on Second Order Conditions in Extreme Value Theory: Linking General and Heavy Tail Conditions
Autor: | M. Isabel Fraga Alves, M. Ivette Gomes, Laurens de Haan, Cláudia Neves |
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Jazyk: | angličtina |
Rok vydání: | 2007 |
Předmět: | |
Zdroj: | Revstat Statistical Journal, Vol 5, Iss 3 (2007) |
Druh dokumentu: | article |
ISSN: | 1645-6726 2183-0371 |
DOI: | 10.57805/revstat.v5i3.53 |
Popis: | Second order conditions ruling the rate of convergence in any first order condition involving regular variation and assuring a unified extreme value limiting distribution function for the sequence of maximum values, linearly normalized, have appeared in several contexts whenever researchers are working either with a general tail, i.e., γ ∈ R, or with heavy tails, with an extreme value index γ > 0. In this paper we shall clarify the link between the second order parameters, say ρ and ρe that have appeared in the two above mentioned set-ups, i.e., for a general tail and for heavy tails, respectively. We illustrate the theory with some examples and, for heavy tails, we provide a link with a third order framework. |
Databáze: | Directory of Open Access Journals |
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