An exhaustive analysis of multiplicative congruential random number generators with modulus 231-1
SIAM Journal on Scientific and Statistical Computing
A guide to simulation (2nd ed.)
A guide to simulation (2nd ed.)
Random number generators: good ones are hard to find
Communications of the ACM
Mathematical aspects of various methods for sampling from classical distributions
WSC '89 Proceedings of the 21st conference on Winter simulation
The ratio of uniforms approach for generating discrete random variates
Journal of Computational and Applied Mathematics - Random numbers and simulation
A fast normal random number generator
ACM Transactions on Mathematical Software (TOMS)
A note on the quality of random variates generated by the ratio of uniforms method
ACM Transactions on Modeling and Computer Simulation (TOMACS)
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A rejection technique for sampling from T-concave distributions
ACM Transactions on Mathematical Software (TOMS)
A rejection technique for sampling from log-concave multivariate distributions
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A sweep-plane algorithm for generating random tuples in simple polytopes
Mathematics of Computation
Computer Generation of Random Variables Using the Ratio of Uniform Deviates
ACM Transactions on Mathematical Software (TOMS)
A simple universal generator for continuous and discrete univariate T-concave distributions
ACM Transactions on Mathematical Software (TOMS)
Proceedings of the 32nd conference on Winter simulation
An automatic code generator for nonuniform random variate generation
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Short universal generators via generalized ratio-of-uniforms method
Mathematics of Computation
Continuous random variate generation by fast numerical inversion
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Simulation for the complex Bingham distribution
Statistics and Computing
A Gaussian Noise Generator for Hardware-Based Simulations
IEEE Transactions on Computers
A compact and accurate Gaussian variate generator
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Fast simulation of truncated Gaussian distributions
Statistics and Computing
Transformed density rejection with inflection points
Statistics and Computing
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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 article 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.