Product Description
In this classic of statistical mathematical theory, Harald Cramér 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 Cramér'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. ... Read more

Customer Reviews (4)

the first great book on mathematical statistics
Princeton University Press originally published this book in the mid 1940s. At the time, Harold Cramer was a leading statistician in Sweden. The field of mathematical statistics was just being formalized and there were no existing books with good mathematical treatment of inference methods. Kolmogorov was developing a rigorous measure theoretic basis for probability while Fisher and Neyman were developing different schools of thought on statistical inference.
Cramer put together the standard reference on mathematical statistics which is still valuable today. This is the type of book to be enjoyed by mathematical statisticians looking at it from a historical perspective. Recent advances require those who need a modern course to study other texts.
Mathematical Statistics made great strides in the 1940s through the 1970s in Europe and America and continues to grow even today.A lot of the the mathematical research in the development of statistical theory can be atrributed to the publication of Cramer's book

not the best book ...
This book is a very old edition. The print quality is not that good. The book is target to real mathematicians, interested in the abstract foundations of probability. I think this was an excellent book in the past, but currently I found a much better book : 'Real analysis and probability' by R.M. Dudley. Dudley 's book is more modern, for instance mentioning banach spaces as the framework for probability. Dudley 's book also provides more rigor and is even more self contained. Cramers book is definetely a 'nice to have' for historical reasons, but if you want an excellent complete explanation of the abstract probability theory, then you definitely must read Dudley ....

not the best book ...
This book is a very old edition. The print quality is not that good. The book is target to real mathematicians, interested in the abstract foundations of probability. I think this was an excellent book in the past, but currently I found a much better book : 'Real analysis and probability' by R.M. Dudley. Dudley 's book is more modern, for instance mentioning banach spaces as the framework for probability. Dudley 's book also provides more rigor and is even more self contained. Cramers book is definetely a 'nice to have' for historical reasons, but if you want an excellent complete explanation of the abstract probability theory, then you definitely must read Dudley ....

A Statistical Toure de Force
This was the first textbook on modern mathematical statistics, and is still one of the best. This work was one of the key elements which transformed probability theory and statistics into rigorous and powerfulbranches of mathematics.

It begins with an introduction to the theory ofintegration and measures, assuming no more than a working knowledge ofcalculus, and is one of the best introductory expositions of measure theoryavailable.

The second part of the book is on statistical inference, andfollows the three giants of modern statistics, Fisher, Neyman and Pearson. Cramér explains the difficult subjects of confidence regions andNeyman-Pearson hypothesis testing clearly and convincingly. The closingportion of the book discuss analysis of variance and linear regressionmethods; and is supplemented with real-world examples throughout, leaningheavily on the data provided by the Swedish census.

This book is aclassic, not least for its combination of lucidity and rigor. Inrecognition of its merits, it has been re-issued in an affordable paperbackedition. It belongs on the shelf of anyone interested in statisticalmethods. ... Read more

Product Description
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 jubliee 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 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 were seminal to the subsequent development of the subject. The collection includes a complete bibliography of Cramer's work. ... Read more

Product Description

Product Description
This is a collection of Harald Cramer's extensive works onnumber theory, probability, mathematical statistics andinsurance mathematics. Many of these are not easily foundnowadays in their original sources, for instance hispioneering works on risk theory published in jublieevolumes of the Skandia Insurance Company in 1930 and 1955.Despite their age, these eminentexamples of Cramer'sexpository style remain highly readable. Cramer was oneofthe "fathers" of modern mathematical statistics. His famousbook onthe subject is still an important reference. Hisstatistical papers includedhere were seminal to thesubsequent development of the subject. The collectionincludes a complete bibliography of Cramer's work. ... Read more

Product Description
Chapters: Sofia Kovalevskaya, Per Martin-Löf, Per Enflo, Lars Hörmander, Harald Cramér, Herman Wold, Henry Wallman, Anders Lindstedt, Olav Kallenberg, Ivar Otto Bendixson, Gösta Mittag-Leffler, Paco Lagerstrom, David Enskog, Waloddi Weibull, Björn Engquist, Lennart Carleson, Filip Lundberg, Germund Dahlquist, Arne Beurling, Albert Victor Bäcklund, Conny Palm, Anders Martin-Löf, Viggo Stoltenberg-Hansen, Anders Björner, Erik Ivar Fredholm, Helge Von Koch, Torkel Franzén, Johan Håstad, Marcel Riesz, Lars Gårding, Oskar Sandberg, Carl Johan Malmsten, Hans Riesel, Samuel Klingenstierna, Torsten Carleman, Thomas Hakon Grönwall, Åke Pleijel, Arne Meurman, Erland Samuel Bring, Fritz Carlson, Toby Gärnö Heikenen. Source: Wikipedia. Pages: 136. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Per Erik Rutger Martin-Löf (born 1942) is a Swedish logician, philosopher, and mathematical statistician. He is internationally renowned for his work on the foundations of probability, statistics, mathematical logic, and computer science. Since the late 1970s, Martin-Löf's publications have been mainly in logic. In philosophical logic, Martin-Löf has wrestled with the philosophy of logical consequence and judgment, partly inspired by the work of Brentano, Frege, and Husserl. In mathematical logic, Martin-Löf has been active in developing intuitionistic type theory as a constructive foundation of mathematics; Martin-Löf's work on type theory has influenced computer science. Per Martin-Löf holds a joint chair for Mathematics and Philosophy at Stockholm University. His brother Anders Martin-Löf is now emeritus professor of mathematical statistics at Stockholm University; the two brothers have collaborated in research in probability and statistics. The research of Anders and Per Martin-Löf has influenced statistic...More: http://booksllc.net/?id=1925764 ... Read more