Asymptotic results for the multiple scan statistic

The contribution of the theory of scan statistics to the study of many real-life applications has been rapidly expanding during the last decades. The multiple scan statistic, defined on a sequence of n Bernoulli trials, enumerates the number of occurrences of k consecutive trials which contain at le...

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Bibliographic Details
Published in:Journal of applied probability 2017-03, Vol.54 (1), p.320-330
Main Authors: Boutsikas, M. V., Koutras, M. V., Milienos, F. S.
Format: Article
Language:English
Subjects:
Poisson distribution
Random walk
Random walk theory
Research Papers
Statistics
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Summary:The contribution of the theory of scan statistics to the study of many real-life applications has been rapidly expanding during the last decades. The multiple scan statistic, defined on a sequence of n Bernoulli trials, enumerates the number of occurrences of k consecutive trials which contain at least r successes among them (r≤k≤n). In this paper we establish some asymptotic results for the distribution of the multiple scan statistic, as n,k,r→∞ and illustrate their accuracy through a simulation study. Our approach is based on an appropriate combination of compound Poisson approximation and random walk theory.
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2016.102