Mathematical methods of statistics

書誌事項

Mathematical methods of statistics

by Harald Cramér

(Princeton landmarks in mathematics and physics)(Princeton paperbacks)

Princeton University Press, 1999

  • : pbk

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注記

Originally published: Uppsala, Sweden : Almqvist & Wiksells, 1945

Includes bibliographical references and index

内容説明・目次

内容説明

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.

目次

Pt. 1Mathematical IntroductionSets of Points3Theory of Measure and Integration in R[subscript 1]19Theory of Measure and Integration in R[subscript n]76Various Questions89Pt. 2Random Variables and Probability DistributionsFoundations137Variables and Distributions in R[subscript 1]166Variables and Distributions in R[subscript n]260Pt. 3Statistical InferenceGeneralities323Sampling Distributions341Tests of Significance, I416Theory of Estimation473Tests of Significance, II525Table 1The Normal Distribution557Table 2The Normal Distribution557Table 3The x[superscript 2]-Distribution559Table 4The t-Distribution560List of References561Index571

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