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

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