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Asymptotic results for the multiple scan statistic

Part of: Limit theorems Distribution theory

Published online by Cambridge University Press:  04 April 2017

M. V. Boutsikas ,
M. V. Koutras  and
F. S. Milienos
M. V. Boutsikas*
Affiliation:
University of Piraeus
M. V. Koutras*
Affiliation:
University of Piraeus
F. S. Milienos*
Affiliation:
University of Piraeus
*
* Postal address: Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli and Dimitriou Street, 18534 Piraeus, Greece.
* Postal address: Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli and Dimitriou Street, 18534 Piraeus, Greece.
* Postal address: Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli and Dimitriou Street, 18534 Piraeus, Greece.
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Abstract

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.

Keywords

Scan statisticcompound Poisson approximationKolmogorov distancetotal variation distanceconvergence in distributionrandom walk

MSC classification

Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 1 , March 2017 , pp. 320 - 330
Copyright
Copyright © Applied Probability Trust 2017 

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