A representation of bivariate extreme value distributions via norms on \(\mathbb{R}^2\) (Q2463698)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A representation of bivariate extreme value distributions via norms on \(\mathbb{R}^2\) |
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A representation of bivariate extreme value distributions via norms on \(\mathbb{R}^2\) (English)
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16 December 2007
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Let \(H_1\) and \(H_2\) be arbitrary univariate extreme value distributions (EVD), let \(\| \cdot\| \) be any norm in \(R^2\). Consider \[ H(s,t)=\exp(-\| (\log(H_1(s)),\log(H_2(t)))\| ). \] Then \(H\) is a bivariate EVD with margins \(H_i\) iff \(\| \cdot\| \) satisfies the condition: \(\forall\;z\in[0,1]\), \(\max(z,1-z)\leq\| (z,1-z)\| \leq 1\).
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Pickands dependence function
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convex set
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copula
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