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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Abstract

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

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

Dates
First available in Project Euclid: 8 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1331216842

Digital Object Identifier
doi:10.1239/jap/1331216842

Mathematical Reviews number (MathSciNet)
MR2952890

Zentralblatt MATH identifier
1236.60016

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

Keywords
Scan statistics Markov chain imbedding random permutation Poisson process

Citation

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. https://projecteuclid.org/euclid.jap/1331216842


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