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Approximation for the Distribution of Three-dimensional Discrete Scan Statistic

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Abstract

We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.’s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan statistics. Importance sampling algorithm is used to obtain sharp bounds for the simulation error. Simulation results and comparisons with other approximations are presented for the binomial and Poisson models.

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Authors and Affiliations

  1. Laboratoire de Mathémathiques Paul Painlevé, UMR 8524, Université de Sciences et Technologies de Lille 1, Cité Scientifique, 59100, Lille, France

    Alexandru Amărioarei & Cristian Preda

  2. INRIA Nord Europe/Modal, 40 avenue Halley, 59650, Villeneuve d’Ascq, France

    Alexandru Amărioarei & Cristian Preda

  3. National Institute of R&D for Biological Sciences, Bucharest, Romania

    Alexandru Amărioarei

Authors
  1. Alexandru Amărioarei
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  2. Cristian Preda
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Correspondence to Alexandru Amărioarei.

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Amărioarei, A., Preda, C. Approximation for the Distribution of Three-dimensional Discrete Scan Statistic. Methodol Comput Appl Probab 17, 565–578 (2015). https://doi.org/10.1007/s11009-013-9382-3

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  • DOI: https://doi.org/10.1007/s11009-013-9382-3

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