Empirical Results

The Tausworthe RNG fails only two tests, the Coupon Collector's test and the 4-27 Birthday Spacings test. We conclude that it is the best RNG amongst the RNGs that we tested. The LCGs (PMMLCG and UNIX) also pass most statistical tests, and are hence suitable for use. TT800 seems to have considerable autocorrelations at lag 2,3,4,8,9 and 10. BBS fails almost all tests and the reasons are discussed in Section 3.5. TrueUniform passes all one-dimensional uniformity tests (in the 1-D $\chi ^2$ test, it has the value 0.4, compared to  4000 of the other RNGs. In the KS test it has 0.0003 compared to  0.8 in the others), however it fails miserably in super-uniformity and randomness tests, as expected.

A possible caveat of our statistical tests is the fact that we were limited by computational resources. Hence we tested only $10^7$ (roughly $2^{23}$) numbers for each RNG. As a result the full periods for most of the RNGs were not exhausted, and it is possible that over their full periods they could have displayed different statistical properties that what we have observed. However, we argue that all RNGs should exhibit good statistical properties within segments of all sizes. Since all RNGs are tested with the same amount of random numbers, we can make fair comparisons about their relative statistical properties and performance.