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In this classic of statistical mathematical theory, Harald Cramer joins the two major lines of development in the field: while 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. The result of Cramer's work is a masterly exposition of the mathematical methods of modern statistics that set the standard that others have since sought to follow.

For anyone with a working knowledge of undergraduate mathematics the book is self contained. The first part is an introduction to the fundamental concept of a distribution and of integration with respect to a distribution. The second part contains the general theory of random variables and probability distributions while the third is devoted to the theory of sampling, statistical estimation, and tests of significance.

--back cover

For anyone with a working knowledge of undergraduate mathematics the book is self contained. The first part is an introduction to the fundamental concept of a distribution and of integration with respect to a distribution. The second part contains the general theory of random variables and probability distributions while the third is devoted to the theory of sampling, statistical estimation, and tests of significance.

--back cover

- GenresMathematics

575 pages, Paperback

First published May 1, 1945

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March 3, 2015

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.

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