Non-Uniform Random Variate Generation by Luc Devroye (PDF)

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User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book gives not only digestible, generator algorithms for the most common distributions I deal with (Poisson, Dirichlet, etc.), but also proofs of their correctness, references for further reading, and an immense amount of theory behind the algorithms, presented in a generalized fashion such that the algorithms could be applied to distributions not described by the book. As a mathematician / computer scientist with a background in algorithms and computational science, this is an invaluable tool. I was expecting a book with a bunch of formulas for generating random variables from various distributions; what I got was that and much, much more. I’m pleasantly surprised and very happy with my purchase.

⭐This book by Luc Devroye is a treasure trove of Monte Carlo simulation recipes many of which are still in use today. It happens that only a limited number of copies were printed by Springer-Verlag, so it is actually a somewhat rare book. A copy of the book from Devroye himself is available in PDF format at the Numerical Recipes website.

⭐One of the still useful great oldies.

⭐Although not dissenting from the other reviews which tout the comprehensiveness of the treatment and its level of detail, I have to add an unpleasant fact about the algorithms: the codes may not work as written, and if they don’t, there’s not an easy way to track down the problem. (This is because of the nature of the constructions used in the complex constant-time algorithms — this opaqueness is not a problem for the elementary algorithms which, alas, may not run in constant time.)A look at the author’s web site (currently at errors.pdf off his main page) shows that, e.g., the algorithm on page 511 for Poisson r.v.’s has four serious bugs. This means that the main algorithm for one of the most important discrete distributions was not coded and tested by the author!In fact, I believe this algorithm has at least one more bug, because I’m still seeing a small off-by-one anomaly in my implementation. The algorithm for binomial r.v.’s may have trouble as well — I see problems for N=400, p=0.05. After 10 million draws (i.e., enough to get good statistics) I see deviations of counts in some bins near the peak (i.e. number of integer outcomes of the R.V.) of *8* standard deviations from the expected number of counts. So, be careful, and consider alternate implementations of the more complex algorithms.

⭐Devroye’s encyclopedic tome on generating random numbers still stands as one of the few masterpieces on the subject. I consult it every time I need to generate random variables beyond the canned standards. Need correlated exponential r.v.s? Devroye gives you multiple methods — and discusses their differences. Correlated beta r.v.s? That’s there too. Brilliant. Unfortunately, the book is out-of-print; fortunately, the author has made the book freely downloadable from his home page.

⭐The book presents many practical algorithms on simulation of both discrete and continuous random variables. It also provides with important information on distributions. It is invaluable for a practitioner interested in using densities arising in applications.

⭐When I had to simulate some non-standard Levy processes I decided to get a book on generating random numbers. The book in question was in my list of many similar books. For “Non-Uniform Random Variate Generation” by L. Devroye there was no table of contents available, so I read all three available reviews (all 5 stars) on the book. Two out of three reviews informed that the author has made the book “freely downloadable from his home page”.Next step is Mr. Devroye home page with many of his personal details and “jokes”. Unfortunately, all my attempts to open any links failed. In one case I was sent to the New Zealand newspaper which informed me that a serial rapist is floating around. I dropped my attempts, for the next joke by Mr. Devroye might be able to attach his favorite virus to the link. I spent my time to confirm a known fact that creative people usually have a finer taste.My advice: unless you are looking for blind surprises try authors who respect their prospective readers.

⭐This 1986 book on simulation methods, that is, on the production of sequences of random variables according to a given probability, remains a mine for all and sundry! The way Luc Devroye analyses each of the presented techniques is deep and (still) original, even some techniques may have aged a bit since the redaction of this fantastic book. For instance, it is unclear avoiding using transcendental functions like log, exp, or cos, is of primary importance when comparing algorithms. I had gone through the book when it appeared, with excitement and eager, but reading back at the current time reveals how much I missed then. Some recent research advances can actually be found therein, even though the authors of such advances are unaware of it. Note that the book is available for free in a high quality pdf format on Luc Devroye’s website.

⭐No problems

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