Chapter 1 discusses methods for generation of basic sequences of pseudorandom numbers that simulate a uniform distribution over the unit interval (0,1).

In Chapter 2, I address some issues of the quality of pseudorandom generators. This discussion had been postponed until after the discussion of Monte Carlo methods in the first edition. (Chapter 2 in this edition is a revision of the first part of Chapter 6 of the first edition.)

Chapter 3 describes some of the basic issues in quasirandom sequences. These sequences are designed to be very regular in covering the support of the random process simulated. (Chapter 3 in this edition is a revision of the second part of Chapter 6 of the first edition.)

Chapter 4 discusses general methods for transforming a uniform random deviate or a sequence of uniform random deviates into a deviate from a different distribution. Chapter 5 describes methods for some common specific distributions. The intent is not to provide a compendium in the manner of Devroye (1986a), but for many standard distributions, to give at least a simple method or two, which may be the best method, but if not, to give references to better methods. Chapter 6 continues the developments of Chapters 4 and 5 to apply them to generation of samples and of nonindependent sequences.

Chapter 7 considers some applications of random numbers. Some of these applications are to solve deterministic problems. This type of method is called Monte Carlo.

Chapter 8 provides information on computer software for generation of random variates. The discussion concentrates on the S-Plus, R, and IMSL software systems.

Monte Carlo methods are widely used in the research literature
to evaluate properties of statistical methods.
Chapter 9 addresses
some of the considerations that apply to this kind of study. I
emphasize that a Monte Carlo study uses an * experiment*, and
the principles of scientific experimentation should be observed.

The literature on the topic of random number generation and Monte Carlo methods is vast and ever-growing. The list of references contains many publications since the publication of the first edition; however, as in the first edition, I do not attempt to provide a comprehensive bibliography. As before, I do not attempt to distinguish the highly-varying quality of the literature.

The main prerequisite for this text is some background in what is generally called ``mathematical statistics''. Some scientific computer literacy is also necessary. I do not use any particular software system in the book, but I do assume the ability to program in either Fortran or C, and the availability of either S-Plus, R, Matlab, or Maple. For some exercises, the required software can be obtained from either statlib or netlib (see the bibliography). In most classes I teach in computational statistics, I give Exercise 9.3 in Chapter 9 as a term project. It is to replicate and extend a Monte Carlo study reported in some recent journal article.

I thank my wife Maria, to whom this book is dedicated, for everything.

I used TeX via LaTeX to write the book, and I used S-Plus and Matlab to generate the graphics. I did all of the typing, programming, etc., myself, so all mistakes are mine. I would appreciate receiving suggestions for improvement and notice of errors.