Stochastic simulation
An exhaustive analysis of multiplicative congruential random number generators with modulus 231-1
SIAM Journal on Scientific and Statistical Computing
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Inversive pseudorandom number generators: concepts, results and links
WSC '95 Proceedings of the 27th conference on Winter simulation
Inversive and linear congruential pseudorandom number generators in empirical tests
ACM Transactions on Modeling and Computer Simulation (TOMACS)
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Fourier Analysis of Uniform Random Number Generators
Journal of the ACM (JACM)
Uniform random number generators
Proceedings of the 30th conference on Winter simulation
On the statistical independence of compound pseudorandom numbers over part of the period
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Asymptotic properties of the spectral test, diaphony, and related quantities
Mathematics of Computation
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In this article, we present a new approach to assessing uniform random number generators, the weighted spectral test, or diaphony. In contrast to the usual spectral test the weighted spectral test is not limited to random number generators with a lattice structure. Its computational complexity is O s˙N2 for any point set of cardinality N in the s-dimensional unit cube. As the main results of this article, we prove an analog of the classical inequality of Erdös-Turán-Koksma, present the necessary tools to transcribe known discrepancy bounds into bounds for diaphony, and provide bounds for the diaphony of multiplicative congruetial pseudorandom numbers. The last section contains numerical results.\