An exhaustive analysis of multiplicative congruential random number generators with modulus 231-1
SIAM Journal on Scientific and Statistical Computing
Uses and abuses of statistical simulation
Mathematical Programming: Series A and B - Mathematical Models and Their Solutions
Efficient and portable combined random number generators
Communications of the ACM
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
Criteria for the assessment of random number generators
Journal of Computational and Applied Mathematics - Random numbers and simulation
Computer Generation of Random Variables Using the Ratio of Uniform Deviates
ACM Transactions on Mathematical Software (TOMS)
The Art of Computer Programming Volumes 1-3 Boxed Set
The Art of Computer Programming Volumes 1-3 Boxed Set
Automatic sampling with the ratio-of-uniforms method
ACM Transactions on Mathematical Software (TOMS)
A simple universal generator for continuous and discrete univariate T-concave distributions
ACM Transactions on Mathematical Software (TOMS)
Gaussian random number generators
ACM Computing Surveys (CSUR)
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The one-dimensional distribution of pseudorandom numbers generated by the ratio of uniforms method using linear congruential generators (LCGs) as the source of uniform random number is investigated in this note. Due to the two-dimensional lattice structure of LCGs there is always a comparable large gap without a point in the one-dimensional distribution of any ratio of uniforms method. Lower bounds for these probabilities only depending on the modulus and the Beyer quotient of the LCG are proved for the case that Cauchy normal or exponential random numbers are generated. These bounds justify the recommendation not to use the ratio of uniform method combined with LCGs.