Skip to main content
SpringerLink
Log in

Estimation for the Distribution of Two-dimensional Discrete Scan Statistics

  • Published:
Methodology and Computing in Applied Probability Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • M. Boutsikas and M. Koutras, “Bounds for the distribution of two dimensional binary scan statistics,” Probability in the Engineering and Information Sciences vol. 17 pp. 509–525, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  • J. Chen and J. Glaz, “Two-dimensional discrete scan statistics,” Statistics and Probability Letters vol. 31 pp. 59–68, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  • J. Glaz, Naus, J., and S. Wallenstein, “Scan Statistics.” In Springer Series in Statistics, Springer: Berlin Heidelberg New York, 2001.

    Google Scholar 

  • G. Haiman, “First passage time for some stationary processes,” Stochastic Processes and their Applications vol. 80(2) pp. 231–248, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  • G. Haiman, “Estimating the distributions of scan statistics with high precision,” Extremes vol. 3(4) pp. 349–361, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  • G. Haiman and C. Preda, “A new method for estimating the distribution of scan statistics for a two-dimensional Poisson process,” Methodology and Computing in Applied Probability vol. 4(4) pp. 393–407, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  • M. Matsumoto and T. Nishimura, “Mersenne twister : A 623—dimensionally equidistributed uniform pseudo-random number generator.” ACM Transactions on Modeling and Computer Simulation vol. 8(1), January 3–30, 1998.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire Paul Painlevé, Université de Lille 1, 59655, Villeneuve d’Ascq, France

    G. Haiman

  2. LSTA Université Paris 6, 59655, Villeneuve d’Ascq, France

    G. Haiman

  3. CERIM-Dépt. de Statistique, Faculté de Médecine Université de Lille 2, 1 Place de Verdun, 59045, Lille, France

    C. Preda

Authors
  1. G. Haiman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Preda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Haiman.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Haiman, G., Preda, C. Estimation for the Distribution of Two-dimensional Discrete Scan Statistics. Methodol Comput Appl Probab 8, 373–382 (2006). https://doi.org/10.1007/s11009-006-9752-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11009-006-9752-1

Keywords

AMS 2000 Subject Classification

Search

Navigation