The Relationship Between the Multiplicative And Mixed Generators Modulo 2^b

MacLaren and Marsaglia [4] comment that their test results suggest that the multiplicative generator performs better than the mixed generator. We attempt to answer the above question by showing that for any sequence of real values in (0,1) produced by the multiplicative generator modulo 2^b a corresponding mixed generator exists which, for practical purposes, produces the same sequence of real values.