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On Wallace's method for the generation of normal variates


Rüb,  Christine
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Rüb, C.(1998). On Wallace's method for the generation of normal variates (MPI-I-1998-1-020). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-7B9B-3
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.