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New maximal inequalities for N-demimartingales with scan statistic applications
Published online by Cambridge University Press: 22 June 2017
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.
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- Copyright © Applied Probability Trust 2017
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