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Approximations for a Three Dimensional Scan Statistic

Author

Listed:
  • Joseph Glaz

    (University of Connecticut)

  • Marco Guerriero

    (University of Connecticut)

  • Rohini Sen

    (University of Connecticut)

Abstract

Let X ijk ,1 ≤ i ≤ N 1,1 ≤ j ≤ N 2, 1 ≤ k ≤ N 3 be a sequence of independent and identically distributed 0 − 1 Bernoulli trials. X ijk = 1 if an event has occurred at the i,j,k th location in a three dimensional rectangular region and X ijk = 0, otherwise. For 2 ≤ m j ≤ N j − 1,1 ≤ j ≤ 3, a three dimensional discrete scan statistic is defined as the maximum number of events in any m 1×m 2×m 3 rectangular sub-region in the entire N 1×N 2×N 3 rectangular region. In this article, a product-type approximation and three Poisson approximations are derived for the distribution of this three dimensional scan statistic. Numerical results are presented to evaluate the accuracy of these approximations and their use in testing for randomness.

Suggested Citation

  • Joseph Glaz & Marco Guerriero & Rohini Sen, 2010. "Approximations for a Three Dimensional Scan Statistic," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 731-747, December.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:4:d:10.1007_s11009-009-9156-0
    DOI: 10.1007/s11009-009-9156-0
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    References listed on IDEAS

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    1. Chen, Jie & Glaz, Joseph, 1996. "Two-dimensional discrete scan statistics," Statistics & Probability Letters, Elsevier, vol. 31(1), pages 59-68, December.
    2. A. D. Barbour & Ourania Chryssaphinou & Malgorzata Roos, 1996. "Compound poisson approximation in systems reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 251-264, March.
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    Cited by:

    1. Alexandru Amărioarei & Cristian Preda, 2015. "Approximation for the Distribution of Three-dimensional Discrete Scan Statistic," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 565-578, September.

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