Convex geometry of max-stable distributions
| dc.creator | Molchanov, Ilya | |
| dc.date | 2006-03-17 | |
| dc.date | 2007-10-29 | |
| dc.date.accessioned | 2026-07-07T08:38:56Z | |
| dc.date.available | 2026-07-07T08:38:56Z | |
| dc.description | It is shown that max-stable random vectors in $[0,\infty)^d$ with unit Fréchet marginals are in one to one correspondence with convex sets $K$ in $[0,\infty)^d$ called max-zonoids. The max-zonoids can be characterised as sets obtained as limits of Minkowski sums of cross-polytopes or, alternatively, as the selection expectation of a random cross-polytope whose distribution is controlled by the spectral measure of the max-stable random vector. Furthermore, the cumulative distribution function $\Prob{ξ\leq x}$ of a max-stable random vector $ξ$ with unit Fréchet marginals is determined by the norm of the inverse to $x$, where all possible norms are given by the support functions of max-zonoids. As an application, geometrical interpretations of a number of well-known concepts from the theory of multivariate extreme values and copulas are provided. The convex geometry approach makes it possible to introduce new operations with max-stable random vectors. | |
| dc.description | 25 pages. Revised version | |
| dc.identifier | https://arxiv.org/abs/math/0603423 | |
| dc.identifier | http://arxiv.org/abs/math/0603423 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140913 | |
| dc.subject | Probability | |
| dc.subject | 60G70; 60D05 | |
| dc.title | Convex geometry of max-stable distributions | |
| dc.type | text |