Abstract
The scan statistic and multiple scan statistic can be used in many areas of science. In this chapter, a survey of results on scan statistic for the continuous conditional case is presented. We discuss the exact distribution and asymptotic results, and study various approximations and bounds. Moreover, a general expression for the kth moment of the multiple scan statistic and a computational approach for its distribution are covered. Numerical results comparing various approximations in the literature are also presented.Keywords and phrasesBonferroni-type inequalitycompound Poisson approximationMarkov chain approximationmultiple scan statisticproduct-type approximationscan statisticspacingsStirling numberssymbolic computation
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