Stochastic ordering in multivariate extremes
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910356410990592 |
|---|---|
| author | Corradini, Michela Strokorb, Kirstin |
| author_facet | Corradini, Michela Strokorb, Kirstin |
| contents | The article considers the multivariate stochastic orders of upper orthants, lower orthants and positive quadrant dependence (PQD) among simple max-stable distributions and their exponent measures. It is shown for each order that it holds for the max-stable distribution if and only if it holds for the corresponding exponent measure. The finding is non-trivial for upper orthants (and hence PQD order). From dimension $d\geq 3$ these three orders are not equivalent and a variety of phenomena can occur. However, every simple max-stable distribution PQD-dominates the corresponding independent model and is PQD-dominated by the fully dependent model. Among parametric models the asymmetric Dirichlet family and the Hüsler-Reiss family turn out to be PQD-ordered according to the natural order within their parameter spaces. For the Hüsler-Reiss family this holds true even for the supermodular order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02039 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stochastic ordering in multivariate extremes Corradini, Michela Strokorb, Kirstin Probability 60G70, 60E15 The article considers the multivariate stochastic orders of upper orthants, lower orthants and positive quadrant dependence (PQD) among simple max-stable distributions and their exponent measures. It is shown for each order that it holds for the max-stable distribution if and only if it holds for the corresponding exponent measure. The finding is non-trivial for upper orthants (and hence PQD order). From dimension $d\geq 3$ these three orders are not equivalent and a variety of phenomena can occur. However, every simple max-stable distribution PQD-dominates the corresponding independent model and is PQD-dominated by the fully dependent model. Among parametric models the asymmetric Dirichlet family and the Hüsler-Reiss family turn out to be PQD-ordered according to the natural order within their parameter spaces. For the Hüsler-Reiss family this holds true even for the supermodular order. |
| title | Stochastic ordering in multivariate extremes |
| topic | Probability 60G70, 60E15 |
| url | https://arxiv.org/abs/2209.02039 |