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Scan Statistics pp 109–128Cite as

Approximations for Two-Dimensional Variable Window Scan Statistics

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Abstract

In this chapter, approximations for distributions of a two- dimensional maximum scan score-type statistic and a minimum p-value scan statistic are derived for independent and identically distributed binomial and Poisson observations. Both unconditional and conditional models are considered. For the conditional models, it is assumed that the total number of observations in the region is known. Numerical results are presented to evaluate the accuracy of the specified probability of Type I error and to compare the power of these variable window-type scan statistics with fixed single window scan statistics.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Massachusetts, Boston, MA, USA

    Jie Chen

  2. Department of Statistics, University of Connecticut, Storrs, CT, USA

    Joseph Glaz

Authors
  1. Jie Chen
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  2. Joseph Glaz
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Editor information

Editors and Affiliations

  1. Dept. Statistics, University of Connecticut, Glenbrook Rd. 215, Storrs, 06269-3120, U.S.A.

    Joseph Glaz

  2. Dept. Statistics, University of Connecticut, Glenbrook Road 215, Storrs, 06269-4120, U.S.A.

    Vladimir Pozdnyakov

  3. Center for Biomathematical Sciences, Mount Sinai School of Medicine, Gustave L Levy Place 1, New York, 10029, U.S.A.

    Sylvan Wallenstein

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© 2009 Birkhäuser Boston, a part of Springer Science+Business Media, LLC

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Chen, J., Glaz, J. (2009). Approximations for Two-Dimensional Variable Window Scan Statistics. In: Glaz, J., Pozdnyakov, V., Wallenstein, S. (eds) Scan Statistics. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4749-0_5

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