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Ratchet Scan and Disjoint Statistics

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Scan Statistics and Applications

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

A general definition of ratchet scan and disjoint statistics is given. The known results for the disjoint statistic, the linear ratchet scan statistic, and the circular ratchet scan statistic are reviewed. This concerns the exact and asymptotic distributions as well as exact bounds for the upper tail probabilities of the test statistics under the null hypothesis of no clustering. Further, results concerning the power of the tests in comparison with other tests for clustering are reported. In addition, certain modifications and extensions, e.g., the EMM procedure, the Grimson models, and the test ofHewitt et al. (1971)are studied. Finally, a general approach to derive exact upper and lower bounds for the tail probabilities of the general ratchet scan statistic is described.

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Author information

Authors and Affiliations

  1. Düsseldorf University, Düsseldorf, Germany

    Joachim Krauth

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  1. Joachim Krauth
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Editors and Affiliations

  1. Department of Statistics, University of Connecticut at Storrs, Storrs, CT, 06269-3120, USA

    Joseph Glaz

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada

    N. Balakrishnan

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Krauth, J. (1999). Ratchet Scan and Disjoint Statistics. In: Glaz, J., Balakrishnan, N. (eds) Scan Statistics and Applications. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1578-3_3

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  • DOI: https://doi.org/10.1007/978-1-4612-1578-3_3

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7201-4

  • Online ISBN: 978-1-4612-1578-3

  • eBook Packages: Springer Book Archive

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