Probability and Statistical Theory for Applied Researchers

Abstract

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 Regression Analysis Readership: Researchers and graduate students in applied fields such as actuarial science, biostatistics, economics, finance, mathematical psychology, and systems engineering. Key Features: Present basic concepts in real and complex analysis and measure theory along with the applications to probability Difficult theoretical points are followed directly by examples and exercises with detailed solutions Provide a survey of Bayesian methods and an extensive treatment of goodness-of-fit tests Suitable learning tool for students and researchers in applied fields for whom a rigorous foundation in probability and statistical inference is essential