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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 [11]. 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 [35], based on the addition of Linear Congruential sequences.
The National Center for Supercomputing Applications
University of Illinois at Urbana-Champaign
ashoks@ncsa.uiuc.edu
Last modified: September 16, 1997