BOUNDS FOR THE DISTRIBUTION OF TWO-DIMENSIONAL BINARY SCAN STATISTICS

  • Authors:

  • Michael V. Boutsikas;Markos V. Koutras

  • Affiliations:

  • Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece, E-mail: mbouts@unipi.gr;Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece, E-mail: mkoutras@unipi.gr

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2003

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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.