Distribution Theory of Runs and Patterns and Its Applications 1st Edition by James Fu, Wendy Wen Yi Lou ISBN 978-9810245870 9810245874
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Product details:
ISBN 10: 9810245874
ISBN 13: 978-9810245870
Author: James C. Fu, Wendy Wen Yi Lou
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.
Table of contents:
Chapter 1 Introduction
Chapter 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
Chapter 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 & 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
Chapter 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
Chapter 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(A)
5.6 More About Generating Functions
5.7 Spectrum Analysis and Large Deviation Approximation
5.8 Probability Generating Function of W(r, A)
5.9 Scan Statistics
Chapter 6 Random Permutations
6.1 Introduction.
6.2 Successions
6.3 Eulerian and Simon Newcomb Numbers
Chapter 7 Applications
7.1 Introduction.
7.2 System Reliability
7.2.1 Consecutive-k-out-of-n:F System
7.2.2 Linearly Connected System
7.3 Hypothesis Testing
7.4 Sequential Continuity
7.5 Quality Control Schemes.
7.5.1 Simple Control Schemes
7.5.2 Compound Control Schemes
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Tags: James Fu, Wendy Wen Yi Lou, Distribution Theory, Runs and Patterns