The purpose of the 3rd edition of this book is to give a sound and self-contained (in the sense that the necessary probability theory is included) introduction to classical or mainstream statistical theory. It is not a statistical-methods-cookbook, nor a compendium of statistical theories, nor is it a mathematics book. The book is intended to be a textbook, aimed for use in the traditional full-year upper-division undergraduate course in probability and statistics, or for use as a text in a course designed for first-year graduate students. The latter course is often a "service course," offered to a variety of disciplines.
No previous course in probability or statistics is needed in order to study the book. The mathematical preparation required is the conventional full-year calculus course which includes series expansion, mUltiple integration, and partial differentiation. Linear algebra is not required. An attempt has been made to talk to the reader. Also, we have retained the approach of presenting the theory with some connection to practical problems. The book is not mathematically rigorous. Proofs, and even exact statements of results, are often not given. Instead, we have tried to impart a "feel" for the theory.
This open book is licensed under a Open Publication License (OPL). You can download Introduction to the Theory of Statistics ebook for free in PDF format (27.6 MB).
Table of Contents
Random Variables, Distribution Functions, and Expectation
Special Parametric Families of Univariate Distributions
Joint and Conditional Distributions, Stochastic Independence, More Expectation
Sampling and Sampling Distributions
Parametric Point Estimation
Parametric Interval Estimation
Tests of Hypotheses