Information Theory And The Central Limit Theorem
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Information Theory and the Central Limit Theorem
Annotation. - Presents surprising, interesting connections between two apparently separate areas of mathematics- Written by one of the researchers who discovered these connections- Offers a new way of looking at familiar results.
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 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 It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems.
A History of the Central Limit Theorem
Author: Hans Fischer
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-10-08
This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.