On the Kolmogorov Distance of Max-Stable Distributions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915565905379328 |
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| author | Hashorva, Enkelejd |
| author_facet | Hashorva, Enkelejd |
| contents | In this contribution, we derive explicit bounds on the Kolmogorov distance for multivariate max-stable distributions with Fréchet margins. We formulate those bounds in terms of (i) Wasserstein distances between de Haan representers, (ii) total variation distances between spectral/angular measures - removing the dimension factor from earlier results in the canonical sphere case - and (iii) discrepancies of the Psi-functions in the inf-argmax decomposition. Extensions to different margins and Archimax/clustered Archimax copulas are further discussed. Examples include logistic, comonotonic, independent and Brown-Resnick models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_18094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Kolmogorov Distance of Max-Stable Distributions Hashorva, Enkelejd Probability Applications Methodology Other Statistics In this contribution, we derive explicit bounds on the Kolmogorov distance for multivariate max-stable distributions with Fréchet margins. We formulate those bounds in terms of (i) Wasserstein distances between de Haan representers, (ii) total variation distances between spectral/angular measures - removing the dimension factor from earlier results in the canonical sphere case - and (iii) discrepancies of the Psi-functions in the inf-argmax decomposition. Extensions to different margins and Archimax/clustered Archimax copulas are further discussed. Examples include logistic, comonotonic, independent and Brown-Resnick models. |
| title | On the Kolmogorov Distance of Max-Stable Distributions |
| topic | Probability Applications Methodology Other Statistics |
| url | https://arxiv.org/abs/2510.18094 |