IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v8y2006i3d10.1007_s11009-006-9752-1.html
   My bibliography  Save this article

Estimation for the Distribution of Two-dimensional Discrete Scan Statistics

Author

Listed:
  • G. Haiman

    (Université de Lille 1
    LSTA Université Paris 6)

  • C. Preda

    (Faculté de Médecine Université de Lille 2)

Abstract

This paper concerns the application of the method introduced in (Haiman, Extremes, 3:349–361, 2000) to estimate the distribution of two-dimensional discrete scan statistics. This method makes it possible to establish sharp bounds for the estimation errors. The method involves the estimation by simulation of the distribution of scan statistics for the particular rectangle sets of size 2×2, 2×3, 3×3, where the unit is the (m 1×m 2) dimension of the rectangular scanning window, m 1, m 2 ∈ℕ. We perform several numerical applications and compare our results with results obtained by other authors.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:3:d:10.1007_s11009-006-9752-1
    DOI: 10.1007/s11009-006-9752-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-006-9752-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-006-9752-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chen, Jie & Glaz, Joseph, 1996. "Two-dimensional discrete scan statistics," Statistics & Probability Letters, Elsevier, vol. 31(1), pages 59-68, December.
    2. 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.
    3. Haiman, George, 1999. "First passage time for some stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 231-248, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Qianzhu Wu & Joseph Glaz, 2019. "Robust Scan Statistics for Detecting a Local Change in Population Mean for Normal Data," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 295-314, March.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Qianzhu Wu & Joseph Glaz, 2019. "Robust Scan Statistics for Detecting a Local Change in Population Mean for Normal Data," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 295-314, March.
    5. Qianzhu Wu & Joseph Glaz, 2021. "Scan Statistics for Normal Data with Outliers," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 429-458, March.
    6. 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.
    7. 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.
    8. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2023. "Reliability of three-dimensional consecutive k-type systems," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    9. Jack Noonan & Anatoly Zhigljavsky, 2021. "Approximations for the Boundary Crossing Probabilities of Moving Sums of Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 873-892, September.
    10. 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.
    11. Chen, Jie & Glaz, Joseph, 2002. "Approximations for a conditional two-dimensional scan statistic," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 287-296, July.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. George Haiman & Cristian Preda, 2010. "A New Method of Approximating the Probability of Matching Common Words in Multiple Random Sequences," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 775-795, December.
    17. George Haiman, 2012. "1-Dependent Stationary Sequences for Some Given Joint Distributions of Two Consecutive Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 445-458, September.
    18. Joseph Glaz & Joseph Naus & Xiao Wang, 2012. "Approximations and Inequalities for Moving Sums," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 597-616, September.
    19. 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.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:8:y:2006:i:3:d:10.1007_s11009-006-9752-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.