Abstract
Glaz and Naus (1991) and Naus (1982) developed tight bounds and sharp approximations for the distribution of the maximum of moving sums of independent and identically distributed integer-valued random variables. These distributions are of importance in a wide variety of applications. To apply the bounds and approximations certain quantities need to be evaluated. We derive new recursive methods to compute efficiently these necessary quantities. An important area of application of our results is testing the significance of regions of high net charge in DNA and Protein sequences. We apply our results to reanalyze a set of data on charges in the Epstein-Barr Virus.
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