Information theory and the central limit theorem /:
This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concer...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
London : River Edge, NJ :
Imperial College Press ; Distributed by World Scientific Pub.,
©2004.
|
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| Summary: | This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concerning their behaviour. It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems. |
| Physical Description: | 1 online resource (xiv, 209 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 199-206) and index. |
| ISBN: | 1860945376 9781860945373 9781860944734 1860944736 |
Staff View
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| 245 | 1 | 0 | |a Information theory and the central limit theorem / |c Oliver Johnson. |
| 260 | |a London : |b Imperial College Press ; |a River Edge, NJ : |b Distributed by World Scientific Pub., |c ©2004. | ||
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| 505 | 0 | |a Information Theory and The Central Limit Theorem; Preface; Contents; 1. Introduction to Information Theory; 2. Convergence in Relative Entropy; 3. Non-Identical Variables and Random Vectors; 4. Dependent Random Variables; 5. Convergence to Stable Laws; 6. Convergence on Compact Groups; 7. Convergence to the Poisson Distribution; 8. Free Random Variables; Appendix A Calculating Entropies; Appendix B Poincare Inequalities; Appendix C de Bruijn Identity; Appendix D Entropy Power Inequality; Appendix E Relationships Between Different Forms of Convergence; Bibliography; Index. | |
| 520 | |a This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concerning their behaviour. It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems. | ||
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| author | Johnson, Oliver (Oliver Thomas) |
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| contents | Information Theory and The Central Limit Theorem; Preface; Contents; 1. Introduction to Information Theory; 2. Convergence in Relative Entropy; 3. Non-Identical Variables and Random Vectors; 4. Dependent Random Variables; 5. Convergence to Stable Laws; 6. Convergence on Compact Groups; 7. Convergence to the Poisson Distribution; 8. Free Random Variables; Appendix A Calculating Entropies; Appendix B Poincare Inequalities; Appendix C de Bruijn Identity; Appendix D Entropy Power Inequality; Appendix E Relationships Between Different Forms of Convergence; Bibliography; Index. |
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| discipline | Mathematik |
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| id | ZDB-4-EBA-ocm60410400 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:35:36Z |
| institution | BVB |
| isbn | 1860945376 9781860945373 9781860944734 1860944736 |
| language | English |
| oclc_num | 60410400 |
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| publishDate | 2004 |
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| spelling | Johnson, Oliver (Oliver Thomas), author. https://id.oclc.org/worldcat/entity/E39PBJxRGWKBTmKDvktyW6qvpP http://id.loc.gov/authorities/names/no2004107330 Information theory and the central limit theorem / Oliver Johnson. London : Imperial College Press ; River Edge, NJ : Distributed by World Scientific Pub., ©2004. 1 online resource (xiv, 209 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references (pages 199-206) and index. Print version record. Information Theory and The Central Limit Theorem; Preface; Contents; 1. Introduction to Information Theory; 2. Convergence in Relative Entropy; 3. Non-Identical Variables and Random Vectors; 4. Dependent Random Variables; 5. Convergence to Stable Laws; 6. Convergence on Compact Groups; 7. Convergence to the Poisson Distribution; 8. Free Random Variables; Appendix A Calculating Entropies; Appendix B Poincare Inequalities; Appendix C de Bruijn Identity; Appendix D Entropy Power Inequality; Appendix E Relationships Between Different Forms of Convergence; Bibliography; Index. This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concerning their behaviour. It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems. Central limit theorem. http://id.loc.gov/authorities/subjects/sh85021905 Information theory Statistical methods. Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Probability https://id.nlm.nih.gov/mesh/D011336 Théorème central limite. Théorie de l'information Méthodes statistiques. Probabilités. probability. aat MATHEMATICS Probability & Statistics General. bisacsh Central limit theorem fast Information theory Statistical methods fast Probabilities fast Print version: Johnson, Oliver (Oliver Thomas). Information theory and the central limit theorem. London : Imperial College Press ; River Edge, NJ : Distributed by World Scientific Pub., ©2004 1860944736 (OCoLC)56905822 |
| spellingShingle | Johnson, Oliver (Oliver Thomas) Information theory and the central limit theorem / Information Theory and The Central Limit Theorem; Preface; Contents; 1. Introduction to Information Theory; 2. Convergence in Relative Entropy; 3. Non-Identical Variables and Random Vectors; 4. Dependent Random Variables; 5. Convergence to Stable Laws; 6. Convergence on Compact Groups; 7. Convergence to the Poisson Distribution; 8. Free Random Variables; Appendix A Calculating Entropies; Appendix B Poincare Inequalities; Appendix C de Bruijn Identity; Appendix D Entropy Power Inequality; Appendix E Relationships Between Different Forms of Convergence; Bibliography; Index. Central limit theorem. http://id.loc.gov/authorities/subjects/sh85021905 Information theory Statistical methods. Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Probability https://id.nlm.nih.gov/mesh/D011336 Théorème central limite. Théorie de l'information Méthodes statistiques. Probabilités. probability. aat MATHEMATICS Probability & Statistics General. bisacsh Central limit theorem fast Information theory Statistical methods fast Probabilities fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85021905 http://id.loc.gov/authorities/subjects/sh85107090 https://id.nlm.nih.gov/mesh/D011336 |
| title | Information theory and the central limit theorem / |
| title_auth | Information theory and the central limit theorem / |
| title_exact_search | Information theory and the central limit theorem / |
| title_full | Information theory and the central limit theorem / Oliver Johnson. |
| title_fullStr | Information theory and the central limit theorem / Oliver Johnson. |
| title_full_unstemmed | Information theory and the central limit theorem / Oliver Johnson. |
| title_short | Information theory and the central limit theorem / |
| title_sort | information theory and the central limit theorem |
| topic | Central limit theorem. http://id.loc.gov/authorities/subjects/sh85021905 Information theory Statistical methods. Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Probability https://id.nlm.nih.gov/mesh/D011336 Théorème central limite. Théorie de l'information Méthodes statistiques. Probabilités. probability. aat MATHEMATICS Probability & Statistics General. bisacsh Central limit theorem fast Information theory Statistical methods fast Probabilities fast |
| topic_facet | Central limit theorem. Information theory Statistical methods. Probabilities. Probability Théorème central limite. Théorie de l'information Méthodes statistiques. Probabilités. probability. MATHEMATICS Probability & Statistics General. Central limit theorem Information theory Statistical methods Probabilities |
| work_keys_str_mv | AT johnsonoliver informationtheoryandthecentrallimittheorem |