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Extensions of Forsythe's method for random sampling from the normal distribution


Authors: J. H. Ahrens and U. Dieter
Journal: Math. Comp. 27 (1973), 927-937
MSC: Primary 65C10
DOI: https://doi.org/10.1090/S0025-5718-1973-0329190-8
MathSciNet review: 0329190
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Abstract: This article is an expansion of G. E. Forsythe's paper "Von Neumann's comparison method for random sampling from the normal and other distributions" [5]. It is shown that Forsythe's method for the normal distribution can be adjusted so that the average number $ \bar{N}$ of uniform deviates required drops to 2.53947 in spite of a shorter program. In a further series of algorithms, $ \bar{N}$ is reduced to values close to 1 at the expense of larger tables. Extensive computational experience is reported which indicates that the new methods compare extremely well with known sampling algorithms for the normal distribution.


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DOI: https://doi.org/10.1090/S0025-5718-1973-0329190-8
Keywords: Random number generation, normal distribution
Article copyright: © Copyright 1973 American Mathematical Society