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Corrected Discrete Approximations for Multiple Window Scan Statistics of One-Dimensional Poisson Processes

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Abstract

In the literature on scan statistics, the distributions of continuous scan statistics for one-dimensional Poisson processes have been extensively studied, most of which deal with single window scan statistics under homogeneous Poisson processes. In this paper, we consider discrete approximations for the distributions of multiple window scan statistics of homogeneous/nonhomogeneous Poisson processes. We derive the first-order terms of the discrete approximations, which involve some functionals of the Poisson processes. We then apply Richardson’s extrapolation to yield corrected (second-order) approximations. Numerical results are presented to show the accuracy of the approximations.

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Acknowledgements

The authors gratefully acknowledge support from the Ministry of Science and Technology of Taiwan, R.O.C.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, 224002, Jiangsu, China

    Yi-Shen Lin

  2. Accounting Information Department, Aletheia University, New Taipei City, 25103, Taiwan, Republic of China

    Xenos Chang-Shuo Lin

  3. Graduate Institute of Finance, National Taiwan University of Science and Technology, Taipei, 106, Taiwan, Republic of China

    Daniel Wei-Chung Miao

  4. Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan, Republic of China

    Yi-Ching Yao

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  1. Yi-Shen Lin
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  2. Xenos Chang-Shuo Lin
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  3. Daniel Wei-Chung Miao
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  4. Yi-Ching Yao
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Correspondence to Yi-Shen Lin.

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Lin, YS., Lin, X.CS., Miao, D.WC. et al. Corrected Discrete Approximations for Multiple Window Scan Statistics of One-Dimensional Poisson Processes. Methodol Comput Appl Probab 22, 237–265 (2020). https://doi.org/10.1007/s11009-019-09704-w

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  • DOI: https://doi.org/10.1007/s11009-019-09704-w

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