Inequalities for the Extremal Coefficients of Multivariate Extreme Value Distributions
Inequalities for the Extremal Coefficients of Multivariate Extreme Value Distributions
复制标题
多元极值分布的极值系数的不等式
DOI：
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发表时间：
2002
期刊：
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通讯作者：
J. Tawn
中科院分区：
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作者：
Martin Schlather;J. Tawn
极值系数是多元极值分布的自然相关性度量。对于 m 变量分布，存在 2m 个不同阶的不同极值系数；它们紧密相连，因此完整的 2m 系数集不能取任意值。我们给出了所有极值系数集的完整特征。为此，我们引入了一类简单的极值分布，它允许 1-1 映射到完整的极值系数集。我们构造高阶极值系数需要满足的边界，以与低阶极值系数保持一致。这些界限很有用，因为低阶极值系数最容易从数据中推断出来。
The extremal coefficients are the natural dependence measures for multivariate extreme value distributions. For an m-variate distribution 2m distinct extremal coefficients of different orders exist; they are closely linked and therefore a complete set of 2m coefficients cannot take any arbitrary values. We give a full characterization of all the sets of extremal coefficients. To this end, we introduce a simple class of extreme value distributions that allows for a 1-1 mapping to the complete sets of extremal coefficients. We construct bounds that higher order extremal coefficients need to satisfy to be consistent with lower order extremal coefficients. These bounds are useful as lower order extremal coefficients are the most easily inferred from data.