Abstract
The scan statistic is used in many areas of science to test the null hypothesis of uniformity against a clustering alternative. In this article product-type approxiamations and Bonferroni-type upper bounds are derived for the tail probabilities of the scan statistic. These new approximations appear to be remarkably accurate and are utilized to compute approximations for the expected size and the standard deviation of the scan statistic. Moreover, accurate approximations are obtained for the distribution and the moments of the smallest interval containing m ordered observations from a uniform distribution in (0,1]. A simulation study is carried out to evaluate the approximations derived in this article.
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