Minimal spacings of non-uniform densities

Jürg Hüsler

Stochastic Processes and their Applications, 1987, vol. 25, 73-81

Abstract: Assume that {Xi, i [greater-or-equal, slanted] 1} is an iid sequence of r.v.'s with distribution F with a density f which has a singularity in one of its end-points of the support. Then we show that the asymptotic behaviour of the minimal spacings, which are the successive differences of the order statistics, is characterized by the behaviour of f in its singularity. We apply these results to coverage problems of the circle and the line, and to the behaviour of the scan-statistic under such a given density.

Keywords: limit; laws; spacings; order; statistics; coverage; circle; line; scan-statistic (search for similar items in EconPapers)
Date: 1987
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