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Two-dimensional discrete scan statistics

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  • Chen, Jie
  • Glaz, Joseph

Abstract

This article investigates the accuracy of approximations for distributions of two-dimensional discrete scan statistics. A product-type approximation, a Bonferroni-type inequality, two Poisson approximations and a compound Poisson approximation are studied. A simulation study is presented to evaluate the accuracy of these approximations. Based on the numerical results it is evident that the standard Poisson approximation can be significantly improved.

Suggested Citation

  • Chen, Jie & Glaz, Joseph, 1996. "Two-dimensional discrete scan statistics," Statistics & Probability Letters, Elsevier, vol. 31(1), pages 59-68, December.
    • Handle: RePEc:eee:stapro:v:31:y:1996:i:1:p:59-68
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    References listed on IDEAS

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    1. James Fu & Markos Koutras, 1994. "Poisson approximations for 2-dimensional patterns," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 179-192, March.
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    Cited by:

    1. Markos V. Koutras & Demetrios P. Lyberopoulos, 2018. "Asymptotic results for jump probabilities associated to the multiple scan statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 951-968, October.
    2. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2023. "Reliability of three-dimensional consecutive k-type systems," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    3. Chen, Jie & Glaz, Joseph, 2002. "Approximations for a conditional two-dimensional scan statistic," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 287-296, July.
    4. 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.
    5. Martin Kulldorff & Zixing Fang & Stephen J Walsh, 2003. "A Tree-Based Scan Statistic for Database Disease Surveillance," Biometrics, The International Biometric Society, vol. 59(2), pages 323-331, June.
    6. Carey E. Priebe & John M. Conroy & David J. Marchette & Youngser Park, 2005. "Scan Statistics on Enron Graphs," Computational and Mathematical Organization Theory, Springer, vol. 11(3), pages 229-247, October.
    7. John Kornak & Mark Irwin & Noel Cressie, 2006. "Spatial Point Process Models of Defensive Strategies: Detecting Changes," Statistical Inference for Stochastic Processes, Springer, vol. 9(1), pages 31-46, May.
    8. 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.
    9. Michael V. Boutsikas & Markos V. Koutras, 2000. "Reliability Approximation for Markov Chain Imbeddable Systems," Methodology and Computing in Applied Probability, Springer, vol. 2(4), pages 393-411, December.

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