Expansions for Quantiles and Multivariate Moments of Extremes for Distributions of Pareto Type
| dc.creator | Nadarajah, Saralees | |
| dc.creator | Withers, Christopher S. | |
| dc.date | 2009-03-25 | |
| dc.date.accessioned | 2026-07-07T12:56:31Z | |
| dc.date.available | 2026-07-07T12:56:31Z | |
| dc.description | Let $X_{nr}$ be the $r$th largest of a random sample of size $n$ from a distribution $F (x) = 1 - \sum_{i = 0}^\infty c_i x^{-α- i β}$ for $α> 0$ and $β> 0$. An inversion theorem is proved and used to derive an expansion for the quantile $F^{-1} (u)$ and powers of it. From this an expansion in powers of $(n^{-1}, n^{-β/α})$ is given for the multivariate moments of the extremes $\{X_{n, n - s_i}, 1 \leq i \leq k \}/n^{1/α}$ for fixed ${\bf s} = (s_1, ..., s_k)$, where $k \geq 1$. Examples include the Cauchy, Student $t$, $F$, second extreme distributions and stable laws of index $α< 1$. | |
| dc.identifier | https://arxiv.org/abs/0903.4391 | |
| dc.identifier | http://arxiv.org/abs/0903.4391 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224610 | |
| dc.subject | Methodology | |
| dc.title | Expansions for Quantiles and Multivariate Moments of Extremes for Distributions of Pareto Type | |
| dc.type | text |