Distribution theory of runs and patterns and its application : a finite Markov chain imbedding approach /
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| Author / Creator: | Fu, James C. |
|---|---|
| Imprint: | [River Edge] New Jersey : World Scientific, c2003. |
| Description: | x, 162 p. : ill. ; 24 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4966398 |
Table of Contents:
- Ch. 1. Introduction
- Ch. 2. Finite Markov Chain Imbedding
- 2.1. Finite Markov Chain
- 2.2. Chapman-Kolmogorov Equation
- 2.3. Tree-Structured Markov Chain
- 2.4. Runs and Patterns
- 2.5. Finite Markov Chain Imbedding
- 2.6. Absorbing State
- 2.7. First-Entry Probability
- Ch. 3. Runs and Patterns in a Sequence of Two-State Trials
- 3.1. Introduction
- 3.2. Number of Non-Overlapping Consecutive k Successes
- 3.3. Number of Success Runs of Length Greater Than or Equal to k
- 3.4. Number of Overlapping Consecutive k Successes
- 3.5. Number of Runs of Exactly k Successes
- 3.6. The Distribution of the Longest Success Run
- 3.7. Waiting-Time Distribution of a Success Run
- 3.8. Numerical Examples
- 3.9. Number of Successes in Success Runs of Length Greater Than or Equal to k
- Ch. 4. Runs and Patterns in Multi-State Trials
- 4.1. Introduction
- 4.2. Forward and Backward Principle with Non-Overlap Counting
- 4.3. Overlap Counting
- 4.4. Series Pattern
- 4.5. Joint Distribution
- Ch. 5. Waiting-Time Distributions
- 5.1. Introduction
- 5.2. The Waiting Time of A Simple Pattern
- 5.3. The Waiting Time of A Compound Pattern
- 5.4. Probability Generating Function
- 5.5. Mean of Waiting Time W([Lambda])
- 5.6. More About Generating Functions
- 5.7. Spectrum Analysis and Large Deviation Approximation
- 5.8. Probability Generating Function of W(r, [Lambda])
- 5.9. Scan Statistics
- Ch. 6. Random Permutations
- 6.1. Introduction
- 6.2. Successions
- 6.3. Eulerian and Simon Newcomb Numbers
- Ch. 7. Applications
- 7.1. Introduction
- 7.2. System Reliability
- 7.3. Hypothesis Testing
- 7.4. Sequential Continuity
- 7.5. Quality Control Schemes.
