On improving pseudo-random number generators

The authors provide some theoretical justifications for the asymptotic uniformity and asymptotic independence of the combination generators without the usual assumption of independence of the generators. The theorems presented give a general method of transforming a possibly bad generator into a much better generator which will yield an asymptotically independent and uniformly distributed random sequence. An empirical study demonstrates that only a small number of terms is required in the author's asymptotic theory to achieve a much more uniform random sequence. As pointed out by S.K. Park and K.W. Miller (1988), some generators provided by certain computer systems may not be very random. Combining several generators into a single generator will provide some protection against the possibility of bad system-provided generators. >