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DISTRIBUTION THEORY OF RUNS AND PATTERNS AND ITS APPLICATIONS
A Finite Markov Chain Imbedding Approach
by James C Fu (University of Manitoba, Canada) & W Y Wendy Lou (University of Toronto, Canada)
This book provides a rigorous, comprehensive introduction to the finite Markov chain imbedding technique for studying the distributions of runs and patterns from a unified and intuitive viewpoint, away from the lines of traditional combinatorics. The central theme of this approach is to properly imbed the random variables of interest into the framework of a finite Markov chain, and the resulting representations of the underlying distributions are compact and very amenable to further study of associated properties. The concept of finite Markov chain imbedding is systematically developed, and its utility is illustrated through practical applications to a variety of fields, including the reliability of engineering systems, hypothesis testing, quality control, and continuity measurement in the health care sector.
Contents:
- Finite Markov Chain Imbedding
- Runs and Patterns in a Sequence of
Two-State Trials
- Runs and Patterns in Multi-State Trials
- Waiting-Time Distributions
- Random Permutations
- Applications
Readership: Graduate students and researchers in probability and statistics.
“Writing a readable account of a particular corner of recent research is never an easy task, but the authors construct a narrative that takes the reader through to the end, while providing enough detail for the exposition to be convincing.”
| Journal of the American Statistical Association |
| 176pp |
Pub. date: Jul 2003 |
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