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A New Method for Estimating the Distribution of Scan Statistics for a Two-Dimensional Poisson Process

Author

Listed:
  • G. Haiman

    (Université de Lille 1
    LSTA Université)

  • C. Preda

    (Université de Lille 2)

Abstract

A method for estimating the distribution of scan statistics with high precisìon was introduced in Haiman (2000). Using that method sharp bounds for the errors were also established. This paper is concerned with the application of the method in Haiman (2000) to a two-dimensional Poisson process. The method involves the estimation by simulation of the conditional (fixed number of points) distribution of scan statistics for the particular rectangle sets of size 2 × 2, 2 × 3, 3 × 3, where the unit is the (1 × 1) dimension of the squared scanning window. In order to perform these particular estimations, we develop and test a “perfect simulation” algorithm. We then perform several numerical applications and compare our results with results obtained by other authors.

Suggested Citation

  • G. Haiman & C. Preda, 2002. "A New Method for Estimating the Distribution of Scan Statistics for a Two-Dimensional Poisson Process," Methodology and Computing in Applied Probability, Springer, vol. 4(4), pages 393-407, December.
    • Handle: RePEc:spr:metcap:v:4:y:2002:i:4:d:10.1023_a:1023518602117
    DOI: 10.1023/A:1023518602117
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    References listed on IDEAS

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    1. Haiman, George, 1999. "First passage time for some stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 231-248, April.
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    Cited by:

    1. Jie Chen & Joseph Glaz, 2016. "Multiple Window Scan Statistics for Two Dimensional Poisson Processes," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 967-977, December.
    2. Jie Chen & Thomas Ferguson & Paul Jorgensen, 2020. "Using Scan Statistics for Cluster Detection: Recognizing Real Bandwagons," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1481-1491, December.
    3. Haiman, George & Preda, Cristian, 2013. "One dimensional scan statistics generated by some dependent stationary sequences," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1457-1463.
    4. G. Haiman & C. Preda, 2006. "Estimation for the Distribution of Two-dimensional Discrete Scan Statistics," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 373-382, September.
    5. Zhao, Bo & Glaz, Joseph, 2016. "Scan statistics for detecting a local change in variance for normal data with unknown population variance," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 137-145.

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