Pickands定理的熵观
An entropic view of Pickands' theorem
摘要：
结果表明，在Renyi-Tsallis最大熵设置中出现的分布与广泛用于建模分布尾部的广义帕累托分布（GPD）有关。这种模型化的相关性，以及GPD在实际情况中的普遍性，来自于关于超额分布（超过高阈值）的Escherema-De Haan-Pickands定理。我们提供了一个熵的观点，这一结果，通过显示，一个适当的归一化过剩变量的分布收敛到最大Tsallis熵，这是GPD的解决方案。这突出了所谓的Tsallis分布在许多应用中的相关性，以及与相应熵的使用的一些相关性。
英文摘要：
It is shown that distributions arising in Renyi-Tsallis maximum entropy setting are related to the Generalized Pareto Distributions (GPD) that are widely used for modeling the tails of distributions. The relevance of such modelization, as well as the ubiquity of GPD in practical situations follows from Balkema-De Haan-Pickands theorem on the distribution of excesses (over a high threshold). We provide an entropic view of this result, by showing that the distribution of a suitably normalized excess variable converges to the solution of a maximum Tsallis entropy, which is the GPD. This highlights the relevance of the so-called Tsallis distributions in many applications as well as some relevance to the use of the corresponding entropy.
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