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One Dimensional Discrete Scan Statistics for Dependent Models and Some Related Problems

Author

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  • Alexandru Amarioarei

    (Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania
    National Institute of Research and Development for Biological Sciences, 060031 Bucharest, Romania)

  • Cristian Preda

    (Laboratoire de Mathématiques Paul Painlevé, University of Lille, 59655 Villeneuve d’Ascq, France
    Biostatistics Department, Delegation for Clinical Research and Innovation, Lille Catholic Hospitals, GHICL, 59462 Lomme, France
    Institute of Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania
    Inria Lille Nord-Europe, MODAL, 59655 Villeneuve d’Ascq, France)

Abstract

The one dimensional discrete scan statistic is considered over sequences of random variables generated by block factor dependence models. Viewed as a maximum of an 1-dependent stationary sequence, the scan statistics distribution is approximated with accuracy and sharp bounds are provided. The longest increasing run statistics is related to the scan statistics and its distribution is studied. The moving average process is a particular case of block factor and the distribution of the associated scan statistics is approximated. Numerical results are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:576-:d:344875
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    References listed on IDEAS

    as
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