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Approximation for the Distribution of Three-dimensional Discrete Scan Statistic

Author

Listed:
  • Alexandru Amărioarei

    (Université de Sciences et Technologies de Lille 1
    INRIA Nord Europe/Modal
    National Institute of R&D for Biological Sciences)

  • Cristian Preda

    (Université de Sciences et Technologies de Lille 1
    INRIA Nord Europe/Modal)

Abstract

We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.’s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan statistics. Importance sampling algorithm is used to obtain sharp bounds for the simulation error. Simulation results and comparisons with other approximations are presented for the binomial and Poisson models.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:3:d:10.1007_s11009-013-9382-3
    DOI: 10.1007/s11009-013-9382-3
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    References listed on IDEAS

    as
    1. 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.
    2. 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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