عنوان

Distribution theory of runs and patterns and its applications :

(Number (ISBN

1281937983

(Number (ISBN

9781281937988

(Number (ISBN

9789812779205

(Number (ISBN

9812779205

Erroneous ISBN

9789810245870

Erroneous ISBN

9810245874

Number

b740260

Title Proper

Distribution theory of runs and patterns and its applications :

General Material Designation

[Book]

Other Title Information

a finite Markov chain imbedding approach /

First Statement of Responsibility

James C. Fu, W.Y. Wendy Lou.

Place of Publication, Distribution, etc.

River Edge, N.J. :

Name of Publisher, Distributor, etc.

World Scientific,

Date of Publication, Distribution, etc.

©2003.

Specific Material Designation and Extent of Item

1 online resource (x, 162 pages) :

Other Physical Details

illustrations

Text of Note

Includes bibliographical references (pages 153-160) and index.

Text of Note

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.

Text of Note

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.

Text of Note

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.

Text of Note

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.

Text of Note

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.

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Text of Note

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.

Title

Distribution theory of runs and patterns and its applications.

International Standard Book Number

9789810245870

Distribution (Probability theory)

Markov processes.

Random variables.

Distribution (Probability theory)

Markov processes.

Mathematical Statistics.

MATHEMATICS-- Probability & Statistics-- Stochastic Processes.

Mathematics.

Physical Sciences & Mathematics.

Random variables.

MAT-- 029040

PBT

Number

Edition

Class number

Book number

Fu, James C.

Lou, W. Y. Wendy.

Date of Transaction

20201204011127.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y