
Mathematical Methods of Statistics
Description
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In 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.
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Content
Sets of Points 3
Theory of Measure and Integration in R[subscript 1] 19
Theory of Measure and Integration in R[subscript n] 76
Various Questions 89
Pt. 2 Random Variables and Probability Distributions
Foundations 137
Variables and Distributions in R[subscript 1] 166
Variables and Distributions in R[subscript n] 260
Pt. 3 Statistical Inference
Generalities 323
Sampling Distributions 341
Tests of Significance, I 416
Theory of Estimation 473
Tests of Significance, II 525
Table 1 The Normal Distribution 557
Table 2 The Normal Distribution 557
Table 3 The x[superscript 2]-Distribution 559
Table 4 The t-Distribution 560
List of References 561
Index 571
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