Publicação
Expansions for Quantiles and Multivariate Moments of Extremes for Heavy Tailed Distributions
| Resumo: | (...)The study of the asymptotes of the moments of Xn,r has been of considerable interest. McCord [12] gave a first approximation to the moments of Xn,1 for three classes. This showed that a moment of Xn,1 can behave like any positive power of n or n1 = log n. (Here, log is to the base e.) Pickands [15] explored the conditions under which various moments of (Xn,1 − bn) /an converge to the corresponding moments of the extreme value distribution. It was proved that this is indeed true for all F in the domain of attraction of an extreme value distribution provided that the moments are finite for sufficiently large n. Nair [13] investigated the limiting behavior of the distribution and the moments of Xn,1 for large n when F is the standard normal distribution function. (...) |
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| Autores principais: | Withers , Christopher |
| Outros Autores: | Nadarajah, Saralees |
| Assunto: | Bell polynomials extremes inversion theorem moments quantiles |
| Ano: | 2017 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | unknown |
| Instituição associada: | Instituto Nacional de Estatística |
| Idioma: | inglês |
| Origem: | REVSTAT-Statistical Journal |
| Resumo: | (...)The study of the asymptotes of the moments of Xn,r has been of considerable interest. McCord [12] gave a first approximation to the moments of Xn,1 for three classes. This showed that a moment of Xn,1 can behave like any positive power of n or n1 = log n. (Here, log is to the base e.) Pickands [15] explored the conditions under which various moments of (Xn,1 − bn) /an converge to the corresponding moments of the extreme value distribution. It was proved that this is indeed true for all F in the domain of attraction of an extreme value distribution provided that the moments are finite for sufficiently large n. Nair [13] investigated the limiting behavior of the distribution and the moments of Xn,1 for large n when F is the standard normal distribution function. (...) |
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