Abstract:We derive explicit comparison bounds for multivariate max-stable distributions with unit-$\alpha$-Fréchet margins. For the Kolmogorov distance, the bounds are expressed through Wasserstein distances between powered de Haan representers, total variation distances between angular measures, and discrepancies of the $\Psi$-functions in the inf--argmax decomposition. On the positive $\ell_\alpha$-sphere, the coefficient multiplying the setwise angular total-variation distance contains no explicit dimension factor for the unnormalised angular measures used here. Separately, for $1\le p<\alpha$, a synchronous de Haan--LePage coupling bounds the $p$-Wasserstein distance between the max-stable laws by an $\alpha$-Wasserstein transport cost between their unpowered de Haan representers. We also compare laws with a common extreme-value copula and different Fréchet indices, obtaining an exact $\ell_1$-Wasserstein formula when $p=1$, and discuss applications to Archimax and clustered Archimax copulas and to Brown--Resnick/Hüsler--Reiss models.
From: Enkelejd Hashorva [view email]
[v1]
Mon, 20 Oct 2025 20:42:06 UTC (20 KB)
[v2]
Fri, 17 Jul 2026 09:00:37 UTC (18 KB)
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