Journal of Applied Probability

Discrete, continuous and conditional multiple window scan statistics

Tung-Lung Wu, Joseph Glaz, and James C. Fu

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 50, Number 4 (2013), 1089-1101.

Dates
First available in Project Euclid: 10 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1389370101

Digital Object Identifier
doi:10.1239/jap/1389370101

Mathematical Reviews number (MathSciNet)
MR3161375

Zentralblatt MATH identifier
1291.60036

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

Keywords
Scan statistic multiple window finite Markov chain imbedding random permutation Poisson process power

Citation

Wu, Tung-Lung; Glaz, Joseph; Fu, James C. Discrete, continuous and conditional multiple window scan statistics. J. Appl. Probab. 50 (2013), no. 4, 1089--1101. doi:10.1239/jap/1389370101. https://projecteuclid.org/euclid.jap/1389370101


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