応用科学研究者のための確率と統計の理論 Probability and Statistical Theory for Applied Researchers

Epps, Thomas Wake

World Scientific Publishing Co Pte Ltd（2013/11発売）

• 製本 Hardcover:ハードカバー版／ページ数 828 p.
• 言語 ENG
• 商品コード 9789814513159
• DDC分類 519.2

Full Description

This book presents the theory of probability and mathematical statistics at a level suitable for researchers at the frontiers of applied disciplines. Examples and exercises make essential concepts in measure theory and analysis accessible to those with preparation limited to vector calculus. Complete, detailed solutions to all the exercises demonstrate techniques of problem solving and provide immediate feedback.Part I, The Theory of Probability, starts with elementary set theory and proceeds through basic measure and probability, random variables, integration and mathematical expectation. It concludes with an extensive survey of models for distributions of random variables. Part II, The Theory of Statistics, begins with sampling theory and distribution theory for statistics from normal populations, proceeds to asymptotic (large-sample) theory, and on to point and interval estimation and tests of parametric hypotheses. The last three chapters cover tests of nonparametric hypotheses, Bayesian methods, and linear and nonlinear regression.Researchers and graduate students in applied fields such as actuarial science, biostatistics, economics, finance, mathematical psychology, and systems engineering will find this book to be a valuable learning tool and an essential reference.

Contents

The Theory of Probability: Probability on Abstract Sets; Probability on Sets of Real Numbers; Mathematical Expectation; Models for Distributions; The Theory of Statistics: Sampling Distributions; Asymptotic Distribution Theory; Estimation; Tests of Parametric Hypotheses; Tests of Nonparametric Hypotheses; A Survey of Bayesian Methods; Modeling Relatedness: Regression Analysis.