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One dimensional scan statistics generated by some dependent stationary sequences

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  • Haiman, George
  • Preda, Cristian

Abstract

We approximate the distribution of scan statistics generated by some Bernoulli and Gaussian stationary 1-dependent models. We compare the results with the corresponding results provided by i.i.d. and Markov models.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:5:p:1457-1463
    DOI: 10.1016/j.spl.2013.02.011
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    References listed on IDEAS

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    1. Morteza Ebneshahrashoob & Tangan Gao & Mengnien Wu, 2005. "An Efficient Algorithm for Exact Distribution of Discrete Scan Statistics," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 459-471, 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. 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.
    4. Haiman, George, 1999. "First passage time for some stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 231-248, April.
    5. 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.
    6. 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.
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    Citations

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    Cited by:

    1. Alexandru Amarioarei & Cristian Preda, 2020. "One Dimensional Discrete Scan Statistics for Dependent Models and Some Related Problems," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    2. Wang, Xiao & Zhao, Bo & Glaz, Joseph, 2014. "A multiple window scan statistic for time series models," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 196-203.
    3. Anat Reiner-Benaim, 2016. "Scan Statistic Tail Probability Assessment Based on Process Covariance and Window Size," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 717-745, September.

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