A History Of The Central Limit Theorem
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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.
Uniform Central Limit Theorems
Author: R. M. Dudley
language: en
Publisher: Cambridge University Press
Release Date: 1999-07-28
This treatise by an acknowledged expert includes several topics not found in any previous book.
A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713-1935
Author: Anders Hald
language: en
Publisher: Springer Science & Business Media
Release Date: 2008-08-24
This is a history of parametric statistical inference, written by one of the most important historians of statistics of the 20th century, Anders Hald. This book can be viewed as a follow-up to his two most recent books, although this current text is much more streamlined and contains new analysis of many ideas and developments. And unlike his other books, which were encyclopedic by nature, this book can be used for a course on the topic, the only prerequisites being a basic course in probability and statistics. The book is divided into five main sections: * Binomial statistical inference; * Statistical inference by inverse probability; * The central limit theorem and linear minimum variance estimation by Laplace and Gauss; * Error theory, skew distributions, correlation, sampling distributions; * The Fisherian Revolution, 1912-1935. Throughout each of the chapters, the author provides lively biographical sketches of many of the main characters, including Laplace, Gauss, Edgeworth, Fisher, and Karl Pearson. He also examines the roles played by DeMoivre, James Bernoulli, and Lagrange, and he provides an accessible exposition of the work of R.A. Fisher. This book will be of interest to statisticians, mathematicians, undergraduate and graduate students, and historians of science.