Automatic Sampling with the Ratio-of-uniforms Method
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
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)
random number generation, non-uniform, rejection method,
ratio of uniforms, log-concave, T-concave,
adaptive method, universal method
© 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.