Description
Book SynopsisHarald 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 tes
Table of Contents
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
