A new empirical test for parallel pseudo-random number generators

Recently, Percus derived probabilities and distributions for parallel, i.i.d. random sequences of integers. This was accomplished by considering s given bit locations in each random variable (represented as a predetermined number of bits) in each sequence. These s bits were used to create a new binary sequence whose expected behavior can be analyzed. Based upon Percus work, an empirical test for parallel pseudo-random number generators has been devised. For each generator, parallel sequences of various lengths are considered and analyzed as proposed by Percus and the results are statistically compared to the expected behavior for truly random sequences. A variety of parallel pseudo-random number generators from the literature are studied and the usefulness of the new empirical test is discussed.