By the numbers

We have presented two methods for generating i.i.d. standard Gaussian random variates, given a function that generates i.i.d. uniform random variates. Given modern computer hardware and software libraries, the Box-Muller transform is likely to be slightly more efficient than the inverse-transform method. Both are very simple to program, provided, in the latter case, that one already has available one of the high-accuracy approximations to F_x ^-1. The inverse-transform method also has appeal in particular specialized applications of Monte Carlo simulation. We have also briefly presented methods for generating i.i.d. sequences of bivariate Gaussian random vectors with correlation p, as well as general multivariate Gaussian random vectors.