Distribution theory of runs and patterns and its applications :: a finite Markov chain imbedding approach /
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 varia...
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| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
River Edge, N.J. :
World Scientific,
©2003.
|
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| 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. |
| Physical Description: | 1 online resource (x, 162 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 153-160) and index. |
| ISBN: | 9789812779205 9812779205 1281937983 9781281937988 |
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MARC
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| 100 | 1 | |a Fu, James C. |0 http://id.loc.gov/authorities/names/n2003010874 | |
| 245 | 1 | 0 | |a Distribution theory of runs and patterns and its applications : |b a finite Markov chain imbedding approach / |c James C. Fu, W.Y. Wendy Lou. |
| 260 | |a River Edge, N.J. : |b World Scientific, |c ©2003. | ||
| 300 | |a 1 online resource (x, 162 pages) : |b illustrations | ||
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| 504 | |a Includes bibliographical references (pages 153-160) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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. | ||
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 650 | 0 | |a Markov processes. |0 http://id.loc.gov/authorities/subjects/sh85081369 | |
| 650 | 0 | |a Random variables. |0 http://id.loc.gov/authorities/subjects/sh85111355 | |
| 650 | 0 | |a Distribution (Probability theory) |0 http://id.loc.gov/authorities/subjects/sh85038545 | |
| 650 | 2 | |a Markov Chains |0 https://id.nlm.nih.gov/mesh/D008390 | |
| 650 | 6 | |a Processus de Markov. | |
| 650 | 6 | |a Variables aléatoires. | |
| 650 | 6 | |a Distribution (Théorie des probabilités) | |
| 650 | 7 | |a distribution (statistics-related concept) |2 aat | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Stochastic Processes. |2 bisacsh | |
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| 650 | 7 | |a Markov processes |2 fast | |
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| 700 | 1 | |a Lou, W. Y. Wendy. |0 http://id.loc.gov/authorities/names/n2003010879 | |
| 758 | |i has work: |a Distribution theory of runs and patterns and its applications (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFBK8cy4JJgHFyyP3MDYvb |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Fu, James C. |t Distribution theory of runs and patterns and its applications. |d River Edge, N.J. : World Scientific, ©2003 |z 9810245874 |z 9789810245870 |w (DLC) 2003053824 |w (OCoLC)52377634 |
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Record in the Search Index
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn261343000 |
|---|---|
| _version_ | 1829094632453046272 |
| adam_text | |
| any_adam_object | |
| author | Fu, James C. |
| author2 | Lou, W. Y. Wendy |
| author2_role | |
| author2_variant | w y w l wyw wywl |
| author_GND | http://id.loc.gov/authorities/names/n2003010874 http://id.loc.gov/authorities/names/n2003010879 |
| author_facet | Fu, James C. Lou, W. Y. Wendy |
| author_role | |
| author_sort | Fu, James C. |
| author_variant | j c f jc jcf |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.7 .F8 2003eb |
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| 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. |
| ctrlnum | (OCoLC)261343000 |
| dewey-full | 519.2/33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/33 |
| dewey-search | 519.2/33 |
| dewey-sort | 3519.2 233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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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. 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| id | ZDB-4-EBA-ocn261343000 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:36:13Z |
| institution | BVB |
| isbn | 9789812779205 9812779205 1281937983 9781281937988 |
| language | English |
| oclc_num | 261343000 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (x, 162 pages) : illustrations |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Fu, James C. http://id.loc.gov/authorities/names/n2003010874 Distribution theory of runs and patterns and its applications : a finite Markov chain imbedding approach / James C. Fu, W.Y. Wendy Lou. River Edge, N.J. : World Scientific, ©2003. 1 online resource (x, 162 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file 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. Markov processes. http://id.loc.gov/authorities/subjects/sh85081369 Random variables. http://id.loc.gov/authorities/subjects/sh85111355 Distribution (Probability theory) http://id.loc.gov/authorities/subjects/sh85038545 Markov Chains https://id.nlm.nih.gov/mesh/D008390 Processus de Markov. Variables aléatoires. Distribution (Théorie des probabilités) distribution (statistics-related concept) aat MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Distribution (Probability theory) fast Markov processes fast Random variables fast Lou, W. Y. Wendy. http://id.loc.gov/authorities/names/n2003010879 has work: Distribution theory of runs and patterns and its applications (Text) https://id.oclc.org/worldcat/entity/E39PCFBK8cy4JJgHFyyP3MDYvb https://id.oclc.org/worldcat/ontology/hasWork Print version: Fu, James C. Distribution theory of runs and patterns and its applications. River Edge, N.J. : World Scientific, ©2003 9810245874 9789810245870 (DLC) 2003053824 (OCoLC)52377634 |
| spellingShingle | Fu, James C. Distribution theory of runs and patterns and its applications : a finite Markov chain imbedding approach / 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. Markov processes. http://id.loc.gov/authorities/subjects/sh85081369 Random variables. http://id.loc.gov/authorities/subjects/sh85111355 Distribution (Probability theory) http://id.loc.gov/authorities/subjects/sh85038545 Markov Chains https://id.nlm.nih.gov/mesh/D008390 Processus de Markov. Variables aléatoires. Distribution (Théorie des probabilités) distribution (statistics-related concept) aat MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Distribution (Probability theory) fast Markov processes fast Random variables fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85081369 http://id.loc.gov/authorities/subjects/sh85111355 http://id.loc.gov/authorities/subjects/sh85038545 https://id.nlm.nih.gov/mesh/D008390 |
| title | Distribution theory of runs and patterns and its applications : a finite Markov chain imbedding approach / |
| title_auth | Distribution theory of runs and patterns and its applications : a finite Markov chain imbedding approach / |
| title_exact_search | Distribution theory of runs and patterns and its applications : a finite Markov chain imbedding approach / |
| title_full | Distribution theory of runs and patterns and its applications : a finite Markov chain imbedding approach / James C. Fu, W.Y. Wendy Lou. |
| title_fullStr | Distribution theory of runs and patterns and its applications : a finite Markov chain imbedding approach / James C. Fu, W.Y. Wendy Lou. |
| title_full_unstemmed | Distribution theory of runs and patterns and its applications : a finite Markov chain imbedding approach / James C. Fu, W.Y. Wendy Lou. |
| title_short | Distribution theory of runs and patterns and its applications : |
| title_sort | distribution theory of runs and patterns and its applications a finite markov chain imbedding approach |
| title_sub | a finite Markov chain imbedding approach / |
| topic | Markov processes. http://id.loc.gov/authorities/subjects/sh85081369 Random variables. http://id.loc.gov/authorities/subjects/sh85111355 Distribution (Probability theory) http://id.loc.gov/authorities/subjects/sh85038545 Markov Chains https://id.nlm.nih.gov/mesh/D008390 Processus de Markov. Variables aléatoires. Distribution (Théorie des probabilités) distribution (statistics-related concept) aat MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Distribution (Probability theory) fast Markov processes fast Random variables fast |
| topic_facet | Markov processes. Random variables. Distribution (Probability theory) Markov Chains Processus de Markov. Variables aléatoires. Distribution (Théorie des probabilités) distribution (statistics-related concept) MATHEMATICS Probability & Statistics Stochastic Processes. Markov processes Random variables |
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