Cramér / Cramer Mathematical Methods of Statistics

Erscheinungsjahr 2016
ISBN: 978-1-4008-8386-8
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 575 Seiten

Reihe: Princeton Mathematical Series

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.

Autoren/Hrsg.

Cramér, Harald

Cramer, Harald

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Pt. 1 Mathematical Introduction

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

Über Autor(innen)

Harald Cramér (1893–1985) was professor of actuarial mathematics and mathematical statistics and director of the Institute of Mathematical Statistics at the University of Stockholm.