Software for uniform random number generation: distinguishing the good and the bad
Proceedings of the 33nd conference on Winter simulation
Testing parallel random number generators
Parallel Computing
Combined generators with components from different families
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
TestU01: A C library for empirical testing of random number generators
ACM Transactions on Mathematical Software (TOMS)
Approximating the tail of the Anderson-Darling distribution
Computational Statistics & Data Analysis
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We study statistical tests of uniformity based on theL p -distances between them nearest pairs of points, forn points generated uniformly over thek-dimensional unit hypercube or unit torus. The number of distinct pairs at distance no more thant, fort = 0, is a stochastic process whose initial part, after an appropriate transformation and asn ? 8, is asymptotically a Poisson process with unit rate. Convergence to this asymptotic is slow in the hypercube as soon ask exceeds 2 or 3, due to edge effects, but is reasonably fast in the torus. We look at the quality of approximation of the exact distributions of the tests statistics by their asymptotic distributions, discuss computational issues, and apply the tests to random number generators. Linear congruential generators fail decisively certain variants of the tests as soon asn approaches the square root of the period length.