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Abstract:
A method proposed by Wallace for the generation of normal random
variates is examined. His method works by transforming a pool
of numbers from the normal distribution into a new pool of number.
This is in contrast to almost all other known methods that transform one
or more variates from the uniform distribution into one or more
variates from the normal distribution. Unfortunately, a direct
implementation of Wallace's method has a serious flaw:
if consecutive numbers produced by this method are added, the
resulting variate, which should also be normally distributed,
will show a significant deviation from the expected behavior.
Wallace's method is analyzed with respect to this deficiency
and simple modifications are proposed that lead to variates of
better quality. It is argued that more randomness (that is,
more uniform random numbers) is needed in the transformation
process to improve the quality of the numbers generated.
However, an implementation of the modified method has
still small deviations from the expected behavior and its running
time is much higher than that of the original.
