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: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Instituto Nacional de Estatística | Statistics Portugal
2017-01-01
|
| Series: | Revstat Statistical Journal |
| Subjects: | |
| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/202 |
| _version_ | 1817998307575726080 |
|---|---|
| author | Christopher Withers Saralees Nadarajah |
| author_facet | Christopher Withers Saralees Nadarajah |
| author_sort | Christopher Withers |
| collection | DOAJ |
| description |
(...)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. (...)
|
| first_indexed | 2024-04-14T02:51:10Z |
| format | Article |
| id | doaj.art-41cda79584ad4a3f83add55f81b202cb |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T02:51:10Z |
| publishDate | 2017-01-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-41cda79584ad4a3f83add55f81b202cb2022-12-22T02:16:16ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712017-01-0115110.57805/revstat.v15i1.202Expansions for Quantiles and Multivariate Moments of Extremes for Heavy Tailed DistributionsChristopher Withers 0Saralees Nadarajah1Industrial Research Limited, Lower HuttUniversity of Manchester (...)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. (...) https://revstat.ine.pt/index.php/REVSTAT/article/view/202Bell polynomialsextremesinversion theoremmomentsquantiles |
| spellingShingle | Christopher Withers Saralees Nadarajah Expansions for Quantiles and Multivariate Moments of Extremes for Heavy Tailed Distributions Revstat Statistical Journal Bell polynomials extremes inversion theorem moments quantiles |
| title | Expansions for Quantiles and Multivariate Moments of Extremes for Heavy Tailed Distributions |
| title_full | Expansions for Quantiles and Multivariate Moments of Extremes for Heavy Tailed Distributions |
| title_fullStr | Expansions for Quantiles and Multivariate Moments of Extremes for Heavy Tailed Distributions |
| title_full_unstemmed | Expansions for Quantiles and Multivariate Moments of Extremes for Heavy Tailed Distributions |
| title_short | Expansions for Quantiles and Multivariate Moments of Extremes for Heavy Tailed Distributions |
| title_sort | expansions for quantiles and multivariate moments of extremes for heavy tailed distributions |
| topic | Bell polynomials extremes inversion theorem moments quantiles |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/202 |
| work_keys_str_mv | AT christopherwithers expansionsforquantilesandmultivariatemomentsofextremesforheavytaileddistributions AT saraleesnadarajah expansionsforquantilesandmultivariatemomentsofextremesforheavytaileddistributions |