This tract develops the purely mathematical side of the theory of probability, without reference to any applications. When originally published, it was one of the earliest works in the field built on the axiomatic foundations introduced by A. Kolmogoroff in his book Grundbegriffe der Wahrscheinlichkeitsrechnung, thus treating the subject as a branch of the theory of completely additive set functions. The author restricts himself to a consideration of probability distributions in spaces of a finite number of dimensions, and to problems connected with the Central Limit Theorem and some of its...

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...

This is a collection of Harald Cramer's extensive work on number theory, probability, mathematical statistics and insurance mathematics. Many of these are not easily found in their original sources nowadays, for instance his pioneering work on risk theory published in the Skandia Insurance Company's jubilee volumes in 1930 and 1955. Despite their age, these eminent examples of Cramer's expository style remain highly readable. Cramer was one of the "fathers" of modern mathematical statistics. His famous book on the subject is still an important reference. His statistical papers included here...

This is a collection of Harald Cramer's extensive works on number theory, probability, mathematical statistics and insurance mathematics. Many of these are not easily found nowadays in their original sources, for instance his pioneering works on risk theory published in jubilee volumes of the Skandia Insurance Company in 1930 and 1955. Despite their age, these eminent examples of Cramer's expository style remain highly readable. Cramer (Stockholm 1893-1985) was one of the "fathers" of modern mathematical statistics. His famous book on the subject is still an important reference. His...