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Approximations for the Distribution and the Moments of Discrete Scan Statistics

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Scan Statistics and Applications

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

LetX 1 ... X N be a sequence of independent and identically distributed nonnegative integer valued random variables. For 2 ≤ m ≤ N, consider the moving sums of m consecutive observations. The discrete scan statistic is defined as the maximum value of these moving sums. Conditional on the sum of all the observations, we refer to this scan statistic as the conditional scan statistic.

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Author information

Authors and Affiliations

  1. University of Massachusetts-Boston, Boston, MA, USA

    Jie Chen & Joseph Glaz

  2. University of Connecticut, Storrs, CT, USA

    Jie Chen & Joseph Glaz

Authors
  1. Jie Chen
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  2. Joseph Glaz
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Editors and Affiliations

  1. Department of Statistics, University of Connecticut at Storrs, Storrs, CT, 06269-3120, USA

    Joseph Glaz

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada

    N. Balakrishnan

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Chen, J., Glaz, J. (1999). Approximations for the Distribution and the Moments of Discrete Scan Statistics. In: Glaz, J., Balakrishnan, N. (eds) Scan Statistics and Applications. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1578-3_2

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  • DOI: https://doi.org/10.1007/978-1-4612-1578-3_2

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7201-4

  • Online ISBN: 978-1-4612-1578-3

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