| Abstrakt: |
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. [ABSTRACT FROM AUTHOR] |
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