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Discrete, Continuous and Conditional Multiple Window Scan Statistics

Part of: Distribution theory - Probability Markov processes

Published online by Cambridge University Press:  30 January 2018

Tung-Lung Wu ,
Joseph Glaz  and
James C. Fu
Tung-Lung Wu*
Affiliation:
University of Connecticut
Joseph Glaz*
Affiliation:
University of Connecticut
James C. Fu*
Affiliation:
University of Manitoba
*
∗ Postal address: Department of Statistics, University of Connecticut, Storrs, CT 06269-4120, USA.
∗ Postal address: Department of Statistics, University of Connecticut, Storrs, CT 06269-4120, USA.
∗∗ Postal address: Department of Statistics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada. Email address: fu@umanitoba.ca
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Abstract

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The distributions of discrete, continuous and conditional multiple window scan statistics are studied. The finite Markov chain imbedding technique has been applied to obtain the distributions of fixed window scan statistics defined from a sequence of Bernoulli trials. In this manuscript the technique is extended to compute the distributions of multiple window scan statistics and the exact powers for multiple pulse and Markov dependent alternatives. An application in blood component quality monitoring is provided. Numerical results are also given to illustrate our theoretical results.

Keywords

Scan statisticmultiple windowfinite Markov chain imbeddingrandom permutationPoisson processpower

MSC classification

Primary: 60E05: Distributions
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 4 , December 2013 , pp. 1089 - 1101
Copyright
© Applied Probability Trust 

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