Automatic Nonuniform Random Variate Generation

This book deals with non-uniform random variate generation algorithms. It is readily accepted that these algorithms are a keystone to stochastic simulation. They are used in all fields of simulation application reaching from computer science, engineering and finance to Bayesian statistics. Even experts in the field of mathematical statistics and probability theory rely on these methods for checking their theoretical results. Nevertheless, the last monographs on random variate generation were published about 15 years ago. But it is not true that research in this area has ceased in recent years. Thus one objective of this text is to demonstrate that —unified under the concept of automatic generators this field comprises lots of recent ideas and developments. As a second objective we want to show that these ideas, little known to most users of simulation till now, are not only based on a nice theory. They also lead to new algorithms that have practical and theoretical advantages in simulation practice. So we tried to find a balance between the necessary mathematical theory and the more applied description of the new algorithms. We also share with the readers our experience concerning the implementation and the numerical problems of the new algorithms. The application of these new algorithms is not difficult due to the freely available UNU.RAN library and the “codegenerator” that can be tested on our web server. This book provides the theoretical background to fully appreciate the advantages of this new automatic approach to random variate generation. Please check our webpage http: //statistik . wu-wien. ac. at/arvag/ that also contains the C code of most of the algorithms of this book and some additional material.