Information theory and the central limit theorem / Oliver Johnson.

Format:

Book

Author/Creator:

Johnson, Oliver (Oliver Thomas)

Language:

English

Subjects (All):

Central limit theorem.

Information theory--Statistical methods.

Information theory.

Probabilities.

Physical Description:

1 online resource (224 p.)

Edition:

1st ed.

Place of Publication:

London : Imperial College Press ; River Edge, NJ : Distributed by World Scientific Publishing, c2004.

Language Note:

English

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 It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems.

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

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 199-206) and index.

ISBN:

9786611866433

9781281866431

1281866431

9781860945373

1860945376

OCLC:

475937135