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