An Introduction to Mathematical Statistics and Its Applications (Larsen & Marx)

Fifth edition, richard-larsen (vanderbilt-university) and morris-marx (university-of-west-florida). Prentice Hall / Pearson Education, © 2012; first edition 1981, then 1986, 2001, 2006, 2012. ~753 pages before the answer key, bibliography and index. LC classification QA276.L314 2012.

Closes the spoke’s statistics and inference growth edge, which had stood since the split: probability-theory was held and inference was not.

What it covers

Fourteen chapters, and the arc is the standard two-semester mathematical-statistics sequence:

1. Introduction — including §1.3, A Brief History, which is unusual in a text of this kind.
2. Probability — sample spaces and the algebra of sets, the probability function, conditional probability, independence, combinatorics, combinatorial probability.
3. Random variables — discrete and continuous, expectation, variance, joint densities, transformations, order statistics, conditional densities, moment-generating functions.
4. Special distributions — Poisson, normal, geometric, negative binomial, gamma; with a proof of the Central Limit Theorem in an appendix.
5. Estimation — maximum likelihood and method of moments, interval estimation, properties of estimators, the Cramér–Rao lower bound, sufficiency, consistency, and Bayesian estimation.
6. Hypothesis testing — the decision rule, Type I and Type II errors, and the generalized likelihood ratio as the notion of optimality.
7. Inferences based on the normal distribution — the t statistic derived rather than asserted, inferences about µ and σ².
8. Types of data: a brief overview — classifying data.
9. Two-sample inferences — µ_X = µ_Y, the F test for variances, binomial two-sample, confidence intervals.
10. Goodness-of-fit tests — multinomial, parameters known and unknown, contingency tables.
11. Regression — least squares, the linear model, covariance and correlation, the bivariate normal.
12. The analysis of variance — the F test, Tukey’s method, subhypotheses with contrasts, data transformations.
13. Randomized block designs — the blocked F test, the paired t test.
14. Nonparametric statistics — sign test, Wilcoxon, Kruskal–Wallis, Friedman, testing for randomness.

The two recurring features

“Taking a Second Look at Statistics” closes every chapter, and these are not summaries. They are short essays on how the machinery misleads — statistical significance versus “practical” significance (§6.6), how not to interpret the sample correlation coefficient (§11.6), samples are not “valid”! (§8.3), outliers (§10.6), Type II error (§7.6). A textbook that spends a section per chapter on the misuse of what it just taught is doing something the corpus’s other texts do not.

Minitab appendices on nearly every chapter. Like hefferon-linear-algebra‘s Sage manual, this names the computational tool the course assumes — and dates it, since Minitab in a 2012 edition is a different assumption from a Python or R one.

Why T1

A Pearson textbook in its fifth edition across 31 years, by two university professors, carrying a Library of Congress record. Same grounds as trench-real-analysis — commercial editorial and review process — and stronger, since this is a current commercial edition rather than a reverted one.

The licence, and it breaks the corpus’s pattern

Worth stating plainly because this spoke has been tracking exactly this. The other five texts here are free by licence: corral-vector-calculus and hefferon-linear-algebra under GFDL/CC, trench-real-analysis under CC BY-NC-SA after its rights reverted, keisler-elementary-calculus CC BY-NC-SA, mcmullen-probability-theory posted by its author on university web space.

This one is not. It is © 2012 Pearson Education, all rights reserved, reproduced as a PDF on an Emory course page. That makes it the first text in the corpus that is accessible without being freely licensed — the two properties the corpus had been treating as one because they had always arrived together. The distinction is now on the record; where it leaves the citation is that this page cites the work, and the course-page URL is where the copy was read, not a licence to it.

Related

richard-larsen · morris-marx · vanderbilt-university · university-of-west-florida · mathematical-statistics · probability-theory · trench-real-analysis · mcmullen-probability-theory · mathematics