Screen LibraryDistribution theory of runs and patterns and its applications : a finite Markov chain imbedding approach /
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 imb...
Saved in:
| Main Authors: | |
|---|---|
| Corporate Authors: | |
| Group Author: | |
| Published: |
World Scientific Pub. Co.,
|
| Publisher Address: | Singapore ; Hackensack, N.J. : |
| Publication Dates: | 2003. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/4669#t=toc |
| Summary: |
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 |
| Carrier Form: | 1 online resource (x,162pages) : illustrations |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9789812779205 (electronic bk.) |
| Index Number: | QA274 |
| CLC: | O211.62 |
| Contents: | ch. 1. Introduction -- ch. 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 -- ch. 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 lo |