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

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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 N ¯ \bar {N} of uniform deviates required drops to 2.53947 in spite of a shorter program. In a further series of algorithms, N ¯ \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.