Journal of Applied Probability

Continuous, discrete, and conditional scan statistics

James C. Fu, Tung-Lung Wu, and W.Y. Wendy Lou

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The distributions for continuous, discrete, and conditional discrete scan statistics are studied. The approach of finite Markov chain imbedding, which has been applied to random permutations as well as to runs and patterns, is extended to compute the distribution of the conditional discrete scan statistic, defined from a sequence of Bernoulli trials. It is shown that the distribution of the continuous scan statistic induced by a Poisson process defined on (0, 1] is a limiting distribution of weighted distributions of conditional discrete scan statistics. Comparisons of rates of convergence as well as numerical comparisons of various bounds and approximations are provided to illustrate the theoretical results.

Article information

J. Appl. Probab., Volume 49, Number 1 (2012), 199-209.

First available in Project Euclid: 8 March 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E05: Distributions: general theory
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Scan statistics Markov chain imbedding random permutation Poisson process


Fu, James C.; Wu, Tung-Lung; Lou, W.Y. Wendy. Continuous, discrete, and conditional scan statistics. J. Appl. Probab. 49 (2012), no. 1, 199--209. doi:10.1239/jap/1331216842.

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