Journal of the American Statistical Association volume 77, issue 377, P177-183 1982 DOI: 10.1080/01621459.1982.10477783 View full text
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Joseph I. Naus

Abstract: Certain statistical applications deal with the extremal distributions of the number of points in a moving interval or window of fixed length. This article gives an approximation that is highly accurate for several of these distributions. Applications include the maximum cluster of points on a line or circle, multiple coverage by subintervals or subarcs of fixed size, the length of the longest success run in Bernoulli trials, and the generalized birthday problem.