Distribution theory of runs and patterns and its application /
James C. Fu, W.Y. Wendy Lou.
- x, 162 p.
Includes bibliographical references and index.
Introduction -- Finite Markov Chain Imbedding -- Finite Markov Chain -- Chapman-Kolmogorov Equation -- Tree-Structured Markov Chain -- Runs and Patterns -- Finite Markov Chain Imbedding -- Absorbing State -- First-Entry Probability -- Runs and Patterns in a Sequence of Two-State Trials -- Introduction -- Number of Non-Overlapping Consecutive k Successes -- Number of Success Runs of Length Greater Than or Equal to k -- Number of Overlapping Consecutive k Successes -- Number of Runs of Exactly k Successes -- The Distribution of the Longest Success Run -- Waiting-Time Distribution of a Success Run -- Numerical Examples -- Number of Successes in Success Runs of Length Greater Than or Equal to k -- Runs and Patterns in Multi-State Trials -- Introduction -- Forward and Backward Principle with Non-Overlap Counting -- Overlap Counting -- Series Pattern -- Joint Distribution -- Waiting-Time Distributions -- Introduction -- The Waiting Time of A Simple Pattern -- The Waiting Time of A Compound Pattern -- Probability Generating Function -- Mean of Waiting Time W([Lambda]) -- More About Generating Functions -- Spectrum Analysis and Large Deviation Approximation -- Probability Generating Function of W(r, [Lambda]) -- Scan Statistics -- Random Permutations -- Introduction -- Successions -- Eulerian and Simon Newcomb Numbers -- Applications -- Introduction -- System Reliability -- Hypothesis Testing -- Sequential Continuity -- Quality Control Schemes. Ch. 1. Ch. 2. 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. Ch. 3. 3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 3.7. 3.8. 3.9. Ch. 4. 4.1. 4.2. 4.3. 4.4. 4.5. Ch. 5. 5.1. 5.2. 5.3. 5.4. 5.5. 5.6. 5.7. 5.8. 5.9. Ch. 6. 6.1. 6.2. 6.3. Ch. 7. 7.1. 7.2. 7.3. 7.4. 7.5.
9810245874 (alk. paper)
2003053824
Markov processes Random variables Distribution (Probability theory)