Mathematical Methods of Statistics

by Harald Cramér

Harald Cramér’s classic synthesis of statistical mathematical theory—an invaluable resource for students and practitioners alikeIn the 1930s, as British and American statisticians were developing the science of statistical inference, French and Russian probabilitists transformed the classical calculus of probability into a rigorous and pure mathematical theory. In this incisive and authoritative book, Harald Cramér unites these two major lines of development, providing a masterly exposition of the mathematical methods of modern statistics that set the standard in the field still followed today.Requiring only a working knowledge of undergraduate mathematics, this self-contained book begins with an introduction to the fundamental concept of a distribution and of integration with respect to a distribution. It goes on to discuss the general theory of random variables and probability distributions, the theory of sampling, statistical estimation, and tests of significance.Blending lucid and accessible writing with mathematical rigor, Mathematical Methods of Statistics belongs on the shelf of anyone interested in statistical methods and remains the standard reference on the subject today.

Genres: Mathematics

575 pages, Kindle Edition

First published May 1, 1945

Reviews

[Douglas · Rating 5 out of 5]

Some say this book is "old" meaning, perhaps, it isn't worth reading by modern students of the subject. But I find it has two qualities that make it worth serious attention. First, it is clearly written. It has one of the best introductions to the Lebesgue theory that you'll find in the literature. Notation is clearly defined and compelling i.e., it makes sense. It uses a minimum of jargon and such as it does use is, for the most part, part of the language of mathematicians as a whole. With notable exceptions, modern treatments, tend to have serious defects in these respects. Second, being one of the first unified treatments of mathematical statistics, it gives the reader a "ground floor" approach to understanding where many subjects came from. I liken it to reading early works on computer science. Today, so much is taken for granted that many students do not know the origins of significant concepts. Thus they tend to minimize the "literary" or "philosophical" issues in favor of modern, high-powered, technique. But with Cramer, following an earlier tradition, there is lots of writing around the symbols, giving one food for thought. Also, his proofs are for the most part compelling and shed light on the subject. Cramer does not hesitate to demure on a proof by referring the reader to a more specialized treatment.