U-max-statistics and limit theorems for perimeters and areas of random polygons

E.V. Koroleva and Yakov Nikitin

Journal of Multivariate Analysis, 2014, vol. 127, issue C, 98-111

Abstract: Recently Lao and Mayer (2008) considered U-max-statistics, where the maximum of kernels over the set of indices is studied instead of the usual sums. Such statistics emerge frequently in stochastic geometry. The examples include the largest distance between random points in a ball, the maximal diameter of a random polygon, the largest scalar product within a sample of points, etc. Their limit distributions are related to the distributions of extreme values.

Keywords: U-max statistics; Weibull distribution; Random perimeter; Random area; Inscribed polygon (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.jmva.2014.02.006

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