Automatic Nonuniform Random Variate Generation

Non-uniform random variate generation is an established research area in the intersection of mathematics, statistics and computer science. Although random variate generation with popular standard distributions have become part of every course on discrete event simulation and on Monte Carlo methods, the recent concept of universal (also called automatic or black-box) random variate generation can only be found dispersed in literature. This new concept has great practical advantages that are little known to most simulation practitioners. Being unique in its overall organization the book covers not only the mathematical and statistical theory, but also deals with the implementation of such methods. All algorithms introduced in the book are designed for practical use in simulation and have been coded and made available by the authors. Examples of possible applications of the presented algorithms (including option pricing, VaR and Bayesian statistics) are presented at the end of the book.

• Markov Chain
• Monte Carlo Methods
• Non-Uniform Random Variate
• Option Pricing
• Random Variate Generation
• Time series
• UNU.RAN library
• VaR
• algorithms
• bayesian statistics

From the reviews:

"The book discusses random variate generation generally, with some emphasis on methods that use the concavity properties of transformations of a density to design rejection algorithms. … Overall, this is a good book that accurately reflects the current state of the art in designing generation algorithms, including many contributions from the authors." (Michael J. Evans, Mathematical Reviews, 2006 b)

"The main topic of the book are universal generators, i.e. the generators usable for a broad class of distributions … . It benefits from the long term research of the authors. All known important methods for the construction of universal nonuniform generators are presented together with the algorithms of corresponding generators. … The book can serve as a monograph and as a textbook. The book is a good choice for everybody interested in nonuniform random number generators." (Jaroslav Král’, Zentralblatt MATH, Vol. 1038 (13), 2004)

"Many statistical methods make use of simulation. … What if we want to simulate from a t-distribution with parameter 2.3? What if the distribution is specified by means of its hazard function? This fascinating book is the place to look for answers to questions such as these. … where the book is particularly interesting is when it presents a variety of ‘automatic methods’. … This book is essential reading for users of simulation and is destined to become a classical reference for the area." (B.J.T. Morgan, Short Book Reviews, Vol. 24 (3), 2004)

"This important book deals with the algorithmic development of the generation of random variables for discrete and continuous ‘large distribution’ families. … The authors introduce a library of algorithms that can generate random variates from a multitude of distributions. These universal generators are termed UNU.RAN and are available from the authors’ Web site. … The mathematics that are introduced are usedintelligently, adding value to the practical edge. The coverage of the literature is comprehensive:-the-best that I have met." (Mohamed Afzal Norat, Journal of the Royal Statistical Society, Vol. 168 (1), 2005)

"This book … has its focus on an area which is usually not covered extensively, namely the search for automatic generators. … The book is also remarkable in that it is both a joy to read for a mathematician and a helpful guidance and reference for practical algorithms. … the text is a comprehensive and well-structured overview over the main ideas and relevant algorithms emanating from them … . It is a welcome and valuable enrichment of the literature about random variate generation … ." (Jakob Creutzig, Metrika, Vol. 64, 2006)

"This book describes approaches to simulating variates from discrete and continuous distributions … . The authors target a mixed audience of computer scientists and statisticians. … Each chapter concludes with an ample number of exercises, and comprehensive references for further study are provided. In summary, I have found this to be a useful reference, and would recommend it to any statistician who regularly engages in (or advises on) simulation studies." (Paul D. Baxter, Journal of Applied Statistics, Vol. 33 (8), 2006)

"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 … . The writing is very clear … and worked examples, often with graphical illustration, facilitate understanding. … I highly recommend this book and the accompanying webpages to graduate students and other researchers from many disciplines (e.g., statistics, computer science, physics, engineering) who need to simulate random variates from non-standard but low-dimensional densities as a part of their research." (Mary Kathryn Cowles, Journal of the American Statistical Association, Vol. 102(479), 2007)

• Dept. of Industrial Engineering, Bogazici University, Istanbul, Turkey

  Wolfgang Hörmann

• Dept. for Applied Statistics & Data Processing, University of Economics and Business Administration, Wien, Austria

  Josef Leydold, Gerhard Derflinger

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