We show how convergence to the Gumbel distribution in an extreme value setting can be understood in an information-theoretic sense. We introduce a new type of score function which behaves well under the maximum operation, and which implies simple expressions for entropy and relative entropy. We show that, assuming certain properties of the von Mises representation, convergence to the Gumbel can be proved in the strong sense of relative entropy.
翻译:我们展示了如何从信息理论的角度理解极端价值环境中与古姆贝尔分布的趋同性。 我们引入了一种新的分数函数,这种函数在最大操作下表现良好,并意味着对英特罗比和相对英特罗比的简单表达方式。 我们显示,假设冯·米斯表示的某些属性,与古姆贝尔的趋同性可以用强烈的相对倍增感来证明。