Mathematical Methods of Statistics

Erscheinungsjahr 1999
ISBN: 978-0-691-00547-8
Verlag: Princeton University Press

Buch, Englisch, Band (PMS-9), 575 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 886 g

Reihe: Princeton Mathematical Series

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.

Autoren/Hrsg.

Cramér, Harald

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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

Über Autor(innen)

Cramér, Harald
Harald Cramér was Professor of Actuarial Mathematics and Mathematical Statistics, and director of the Institute of Mathematical Statistics at the University of Stockholm.