Automatic Sampling with the Ratio-of-uniforms Method

Josef Leydold


Applying the ratio-of-uniforms method for generating random variates results in very efficient, fast and easy to implement algorithms. However parameters for every particular type of density must be precalculated analytically. In this paper we show, that the ratio-of-uniforms method is also useful for the design of a black-box algorithm suitable for a large class of distributions, including all with log-concave densities. Using polygonal envelopes and squeezes results in an algorithm that is extremely fast. In opposition to any other ratio-of-uniforms algorithm the expected number of uniform random numbers is less than two. Furthermore we show that this method is in some sense equivalent to transformed density rejection.

CR Categories and Subject Descriptors: G.3 [Probability and Statistics]: Random number generation

Mathematics Subject Classification: 65C10 (Random Number Generation); 65U05 (Numerical methods in probability and statistics), 11K45 (Pseudo-random numbers, Monte Carlo methods)

General Terms: Algorithms

Key Words: random number generation, non-uniform, rejection method, ratio of uniforms, log-concave, T-concave, adaptive method, universal method

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© ACM, (1998). This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Trans. Math. Softw. 26(1), 78 - 98. http://doi.acm.org/10.1145/347837.347863