Limit Distributions for Sums of Independent Random Vectors

between this viewpoint and that adopted by the popular industrial engineering text Factory Physics (Hopp and Spearman 2000). In any case, this philosophy leads to the extensive use of mini-experiments and projects, most of which can be carried out quite easily in Mathematica (or any other similar algebraic manipulation package). The book includes a CD with the software package Mathematica Uncertain Virtual Worlds. The second major difference between this book and others is organizational. It is divided into three parts: I, “Descriptive Statistics—Compressing Data;” II, “Modeling Uncertainty;” and III, “Model Speci cation—Design of Experiments. ” First, the descriptive analysis portion of the text is a great deal more thorough than one might  nd elsewhere. Along the way, the authors present an impressive array of examples illustrating the need for data analysis (Chap. 1), a number of methods to represent and compress data (Chap. 2), and  nally some distributional theory (Chap. 3). Some welcome surprises in this portion include an excellent synopsis on pseudo-random number and random variate generation, chaos and fractals, and early discussions of con dence intervals and hypothesis testing (in the context of Bernoulli parameter estimation), as well as the Kolmogorov–Smirnov (K–S) goodness-of- t test, which most texts delay until later. The second portion, on the modeling of uncertainty, is the text’s most unique. Chapter 4 consists of a wonderful presentation on randomness, where the discussion cuts a wide swath through complexity theory and probability theory. We  nd well-written, succinct material on everything from ® ° -completeness to Kolmogorov complexity to Gödel’s incompleteness theorem to Martin–Löf tests of randomness. Chapter 5’s presentations on independence, expectation, and the central limit theorem are more typical of those found in a standard text. The very nice and self-contained Chapter 6, dealing with chaos in dynamical systems, rounds out this section of the text. Here the authors use  xed-point theory and fractals (among other interesting techniques) to handle the uncertainty that arises in various engineering phenomena. The topic areas of the third part of the text are somewhat more standard than those already encountered. In particular, separate chapters are devoted to estimation (Chap. 7); con dence intervals and hypothesis testing (mostly for normal data), regression, and goodness of  t (Chap. 8); and singleand two-factor ANOVA (Chap. 9). Thus, this book covers most of the topics that one would want to teach in a standard introductory probability and statistics course—albeit, perhaps, in a different order. What makes the book a special success is that it emphasizes these topics from both traditional and computational standpoints, with plenty of interesting Mathematica experiments and projects to motivate the student. These include examples on the distribution of stars, DNA sequencing, elementary queueing theory, faculty salaries, computation of the K–S distribution function, the Mandelbrot set, and Monte Carlo simulation. In addition, every chapter contains problem sets that run the gamut from small programming exercises to more open-ended projects. The Mathematica examples are presented in a style and order that will allow the student to pick up the necessary programming skills while progressing through the book. Further, a website, http://www.birkhauser. com/book/isbn/ 0-8176-4031-2, contains a great deal of downloadable material, mostly in the form of datasets and code, that should prove useful to the student. In short, Introductory Statistics and Random Phenomena is well written, interesting, and unique among statistics texts in that it certainly approaches the topic from a new perspective. This is an excellent text that I believe professors and students will enjoy and bene t from using.