Mathematical Methods of Statistics Pms 9 Volume 9 Harald Cramér 1400883865 9781400883868

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Product details:

• ISBN 10: 1400883865
• ISBN 13: 9781400883868
• Author: Harald Cramér

Harald Cramér’s classic synthesis of statistical mathematical theory—an invaluable resource for students and practitioners alike 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.

Table of contents:

1. Chapter 1. General properties of sets
2. Chapter 2. Linear point sets
3. Chapter 3. Point sets in n dimensions
4. Chapter 4. The Lebesgue measure of a linear point set
5. Chapter 5. The Lebesgue integral for functions of one variable
6. Chapter 6. Non-negative additive set functions in R1
7. Chapter 7. The Lebesgue-Stieltjes integral for functions of one variable
8. Chapter 8. Lebesgue measure and other additive set functions in Rn
9. Chapter 9. The Lebesgue-Stieltjes integral for functions of n variables
10. Chapter 10. Fourier integrals
11. Chapter 11. Matrices, determinants and quadratic forms
12. Chapter 12. Miscellaneous complements
13. Chapter 13. Statistics and probability
14. Chapter 14. Fundamental definitions and axioms
15. Chapter 15. General properties
16. Chapter 16. Various discrete distributions
17. Chapter 17. The normal distribution
18. Chapter 18. Various distributions related to the normal
19. Chapter 19. Further continuous distributions
20. Chapter 20. Some convergence theorems
21. Chapter 21. The two-dimensional case
22. Chapter 22. General properties of distributions in Rn
23. Chapter 23. Regression and correlation in n variables
24. Chapter 24. The normal distribution
25. Chapter 25. Preliminary notions on sampling
26. Chapter 26. Statistical inference
27. Chapter 27. Characteristics of sampling distributions
28. Chapter 28. Asymptotic properties of sampling distributions
29. Chapter 29. Exact sampling distributions
30. Chapter 30. Tests of goodness of fit and allied tests
31. Chapter 31. Tests of significance for parameters
32. Chapter 32. Classification of estimates
33. Chapter 33. Methods of estimation
34. Chapter 34. Confidence regions
35. Chapter 35. General theory of testing statistical hypotheses
36. Chapter 36. Analysis of variance

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