Mathematical Statistics with Mathematica, by Colin

This book is an accompaniment to the computer software package mathStatica (which runs as an add-on to Mathematica). The book comes with two CD-ROMS: mathStatica, and a 30-day trial version of Mathematica 4.1. The mathStatica CD-ROM includes an applications pack for doing mathematical statistics, custom Mathematica palettes and an electronic version of the book that is identical to the printed text, but can be used interactively to generate animations of some of the book's figures (e.g. as a parameter is varied). (I found this last feature particularly valuable.) MathStatica has statistical operators for determining expectations (and hence characteristic functions, for example) and probabilities, for finding the distributions of transformations of random variables and generally for dealing with the kinds of problems and questions that arise in mathematical statistics. Applications include estimation, curve-fitting, asymptotics, decision theory and moment conversion formulae (e.g. central to cumulant). To give an idea of the coverage of the book: after an introductory chapter, there are three chapters on random variables, then chapters on systems of distributions (e.g. Pearson), multivariate distributions, moments, asymptotic theory, decision theory and then three chapters on estimation. There is an appendix, which deals with technical Mathematica details. What distinguishes mathStatica from statistical packages such as S-PLUS, R, SPSS and SAS is its ability to deal with the algebraic/symbolic problems that are the main concern of mathematical statistics. This is, of course, because it is based on Mathematica, and this is also the reason that it has a note–book interface (which enables one to incorporate text, equations and pictures into a single line), and why arbitrary-precision calculations can be performed. According to the authors, 'this book can be used as a course text in mathematical statistics or as an accompaniment to a more traditional text'. Assumed knowledge includes preliminary courses in statistics, probability and calculus. The emphasis is on problem solving. The material is supposedly pitched at the same level as Hogg and Craig (1995). However some topics are treated in much more depth than in Hogg and Craig (characteristic functions for instance, which rate less than one page in Hogg and Craig). Also, the coverage is far broader than that of Hogg and Craig; additional topics include for instance stable distributions, cumulants, Pearson families, Gram-Charlier expansions and copulae. Hogg and Craig can be used as a textbook for a third-year course in mathematical statistics in some Australian universities , whereas there is …