Probability And Statistical Models

With an emphasis on models and techniques, this textbook introduces many of the fundamental concepts of stochastic modeling that are now a vital component of almost every scientific investigation. These models form the basis of well-known parametric lifetime distributions such as exponential, Weibull, and gamma distributions, as well as change-point and mixture models.

An outgrowth of the sixth conference on “Mathematical Methods in Reliability: Theory, Methods, and Applications,” this book is a selection of invited chapters, all of which deal with various aspects of mathematical and statistical models and methods in reliability.

This book is in two volumes, and is intended as a text for introductory courses in probability and statistics at the second or third year university level. It emphasizes applications and logical principles rather than math­ ematical theory. A good background in freshman calculus is sufficient for most of the material presented. Several starred sections have been included as supplementary material. Nearly 900 problems and exercises of varying difficulty are given, and Appendix A contains answers to about one-third of them.

A comprehensive text and reference bringing together advances in the theory of probability and statistics and relating them to applications. The three major categories of statistical models that relate dependent variables to explanatory variables are covered: univariate regression models, multivariate regression models, and simultaneous equations models. Methods are illustrated with worked examples, complete with figures that display code and output.