The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
An Efficient Method for Generating Discrete Random Variables with General Distributions
ACM Transactions on Mathematical Software (TOMS)
Computer Generation of Random Variables Using the Ratio of Uniform Deviates
ACM Transactions on Mathematical Software (TOMS)
Algorithm 488: A Gaussian pseudo-random number generator
Communications of the ACM
Generating discrete random variables in a computer
Communications of the ACM
Discrete univariate random variate generation
WSC '83 Proceedings of the 15th conference on Winter simulation - Volume 1
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The alias-rejection-mixture method is a general and exact method for the computer generation of random variables from an arbitrary discrete, continuous, or mixed probability distribution. The method is based on two ingredients: (1) Walker's alias method, an ingenious and efficient method for generating discrete random variables, and (2) the rejection-mixture method, which is a modification of the standard rejection method that eliminates the need to repeat steps of the algorithm. The generation of random variables by the alias-rejection-mixture method requires operations that are simple and few and, remarkably, approximately the same for all distributions.