Better quality sequences can often be obtained by combining the output
of the basic generators to create a new random sequence as follows:
where is typically either the exclusive-or operator or addition modulo some integer m, and x and y are sequences from two independent generators. It is best if the cycle length of the two generators is relatively prime, for this implies that the cycle length of z will be the product of that of the basic generators. One can show that the statistical properties of z are no worse than those of x or y . In fact, one expects it would be much superior but little has yet been proven to date.
Good combined generators have been developed by L'Ecuyer , based on the addition of Linear Congruential sequences.
The National Center for Supercomputing Applications
University of Illinois at Urbana-Champaign
Last modified: September 16, 1997