Non-uniform random variate generation is a small field of research somewhere between mathematics, statistics and computer science. It started in the fifties of the last century in the “stone-age” of computers. Since then its development has mainly been driven by the wish of researchers to solve generation problems necessary to run their simulation models. Also the need for fast generators has been an important driving force. The main mathematical problems that have to be solved concern the distribution of transformed random variates and finding tight inequalities. Also implementing and testing the proposed algorithms has been an important part of the research work. A large number of research papers in this field has been published in the seventies and early eighties. The main bibliographical landmark of this development is the book of Devroye (1986a), that is commonly addressed as the “bible” of random variate generation. We can certainly say that random variate generation has become an accepted research area considered as a subarea of statistical computing and simulation methodology. Practically all text-books on discrete event simulation or Monte Carlo methods include at least one chapter on random variate generation; within simulation courses it is taught even to undergraduate students.
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