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Distribution theory of runs and patterns and its applications : a finite Markov chain imbedding approach / James C. Fu, W.Y. Wendy Lou.

By: Fu, James CContributor(s): Lou, W. Y. WendyMaterial type: TextTextPublication details: River Edge, N.J. : World Scientific, ©2003. Description: 1 online resource (x, 162 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9789812779205; 9812779205; 1281937983; 9781281937988Subject(s): Markov processes | Random variables | Distribution (Probability theory) | MATHEMATICS -- Probability & Statistics -- Stochastic Processes | Distribution (Probability theory) | Markov processes | Random variables | Mathematical Statistics | Mathematics | Physical Sciences & MathematicsGenre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: Distribution theory of runs and patterns and its applications.DDC classification: 519.2/33 LOC classification: QA274.7 | .F8 2003ebOnline resources: Click here to access online
Contents:
Preface ; 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 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.
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.
Summary: 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.
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Includes bibliographical references (pages 153-160) and index.

Print version record.

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.

Preface ; 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 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.

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.

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