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BOUNDS FOR THE DISTRIBUTION OF TWO-DIMENSIONAL BINARY SCAN STATISTICS

Published online by Cambridge University Press:  24 September 2003

Michael V. Boutsikas  and
Markos V. Koutras
Michael V. Boutsikas
Affiliation:
Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece, E-mail: mbouts@unipi.gr
Markos V. Koutras
Affiliation:
Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece, E-mail: mkoutras@unipi.gr
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Abstract

In the present article, we develop some efficient bounds for the distribution function of a two-dimensional scan statistic defined on a (double) sequence of independent and identically distributed (i.i.d.) binary trials. The methodology employed here takes advantage of the connection between the scan statistic problem and an equivalent reliability structure and exploits appropriate techniques of reliability theory to establish tractable bounds for the distribution of the statistic of interest. An asymptotic result is established and a numerical study is carried out to investigate the efficiency of the suggested bounds.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 17 , Issue 4 , October 2003 , pp. 509 - 525
Copyright
© 2003 Cambridge University Press

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