Automatic Nonuniform Random Variate Generation

摘要

Automatic Nonuniform Random Variate Generation is primarily a research monograph unifying the authors' work in algorithms and software to sample from a large family of distributions—discrete, continuous, univariate, and mul tivariate. The authors have used parts of the book in their courses on random variate generation and simulation. Chapters 2 and 3 provide an introduction to general principles and methods of univariate random variate generation: inversion, rejection, composition, and ratio-of-uniforms methods. Similarly, Chapter 11 begins with general principles for generating random vectors. The emphasis is on mathematical concepts and algorithms, rather than implementation in any particular computer language or environment. The presentation is in the form of theorems (with proofs provided unless measure theory is required, in which case references containing the proofs are given) and concise algorithms in pseudocode. The book does not assume previous experience with random variate generation; in fact, the only mathematical background required is calculus and probability. Exercises are provided for all but one of the 15 chapters. (Solutions do not appear to be available either in the book itself or on the accompanying web page, however.) Like the book content, the exercises involve concepts rather than computer code; for example, "Spell out the details of the inversion algorithm to generate from the Laplace density, which is proportional to e~(|x|) (p. 39). The writing is very clear (although occasionally the English is not perfectly colloquial), and worked examples, often with graphical illustration, facilitate understanding. However, for general use in a graduate course on random variate generation and simulation methods, a text such as that of Gentle (1998) probably would be more appropriate.