Expansions for Quantiles and Multivariate Moments of Extremes for Heavy Tailed Distributions
(...)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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2017-01-01
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| Series: | Revstat Statistical Journal |
| Subjects: | |
| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/202 |
| Summary: | (...)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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| ISSN: | 1645-6726 2183-0371 |