Abstract

Recently, W. Lao and M. Mayer (2008) developed U-max-statistics, where instead of averaging the values of the kernel over various subsets, the maximum of the kernel is considered. Such statistics often appear in stochastic geometry. Their limit distributions are related to the distributions of extreme values. In this paper, we begin to consider the limit theorems for the generalized perimeter (the sum of side powers) of a random inscribed polygon and U-max-statistics related to it. We describe extreme values of the generalized perimeter and obtain limit theorems for the cases where the side powers involved in determining the generalized perimeter do not exceed 1.

中文翻译：

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随机内接多边形的广义周界的极限定理。一世

摘要

最近，W。Lao和M. Mayer（2008）开发了U -max-statistics，其中考虑了内核的最大值，而不是对各个子集上的内核值取平均值。这种统计通常以随机几何形式出现。它们的极限分布与极值的分布有关。在本文中，我们开始考虑随机内接多边形的广义周长（边功率之和）的极限定理及其相关的U -max统计量。我们描述了广义周长的极值，并获得了用于确定广义周长的边功率不超过1的情况的极限定理。