Abstract:In the present work, some new maximal inequalities for nonnegative N-demi(super)martingales are first developed. As an application, new bounds for the cumulative distribution function of the waiting time for the first occurrence of a scan statistic in a sequence of independent and identically distributed (i.i.d.) binary trials are obtained. A numerical study is also carried out for investigating the behavior of the new bounds.
In this paper, we review a number of bounds and approximations for the distribution of the multiple scan statistic defined on a sequence of binary trials. Using a simulation study, we proceed to the assessment of the accuracy of the approximations.
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