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For computer simulations, it is often useful to generate values that have a normal distribution.

There are several methods; the most basic is to invert the standard normal cdf. More efficient methods are also known.

One such method is the Box-Muller transform.

The Box-Muller transform takes two uniformly distributed values as input and maps them to two normally distributed values.

This requires generating values from a uniform distribution, for which many methods are known. See also random number generators.

The Box-Muller transform is a consequence of Property 3 and the fact that the chi-square distribution with two degrees of freedom is an exponential random variable (which is éasy to generate).