Stochastic simulation
An exhaustive analysis of multiplicative congruential random number generators with modulus 231-1
SIAM Journal on Scientific and Statistical Computing
Random number generators: good ones are hard to find
Communications of the ACM
Random number generators for parallel processors
Journal of Computational and Applied Mathematics - Random numbers and simulation
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Testing random number generators
WSC '92 Proceedings of the 24th conference on Winter simulation
Improved lower bounds for the discrepancy of inversive congruential pseudorandom numbers
Mathematics of Computation
On a new class of pseudorandom numbers for simulation methods
Journal of Computational and Applied Mathematics
Some linear and nonlinear methods for pseudorandom number generation
WSC '95 Proceedings of the 27th conference on Winter simulation
Fourier Analysis of Uniform Random Number Generators
Journal of the ACM (JACM)
The Art of Computer Programming Volumes 1-3 Boxed Set
The Art of Computer Programming Volumes 1-3 Boxed Set
Radix-b extensions to some common empirical tests for pseudorandom number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Uniform random number generators: a review
Proceedings of the 29th conference on Winter simulation
The weighted spectral test: diaphony
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Bad subsequences of well-known linear congruential pseudorandom number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Statistical independence properties of inversive pseudorandom vectors over parts of the period
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on modeling and analysis of stochastic systems
Uniform random number generators
Proceedings of the 30th conference on Winter simulation
Parallel streams of linear random numbers in the spectral test
ACM Transactions on Modeling and Computer Simulation (TOMACS)
TestU01: A C library for empirical testing of random number generators
ACM Transactions on Mathematical Software (TOMS)
A compact and accurate Gaussian variate generator
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Fast and small nonlinear pseudorandom number generators for computer simulation
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
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Stochastic simulation requires a reliable source of randomness. Inversive methods are an interesting and very promising new approach to produce uniform pseudorandom numbers. In this paper, we present evidence that these methods are an important contribution to our toolbox. We survey the outstanding performance of inversive pseudorandom number generators in theoretical and empirical tests, in comparison to linear generators. In addition, this paper contains tables of parameters to implement inversive congruential generators.