Statistical tests of some widely used and recently proposed uniform random number generators

摘要

Several widely used uniform random number generators have been extensivelysubjected to three commonly used statistical tests of uniformityand randomness. The object was i) to examine the power of these statisticaltests to discriminate between "good" and "bad" random number generators,ii) to correlate these results with recently proposed mathematicalcharacterizations of random number generators which might also be usefulin such a discrimination, and iii) to examine the effect of shuffling onthe random number generators.Briefly the results show that the commonly used runs test has virtuallyno power to discriminate between "good" and "bad" generators, whileserial tests perform better. Also shuffling does help, although muchmore needs to be done in this area. And finally, there is some utilityto the mathematical characterizations, but many unanswered questions.