In this procedure for generating random numbers with the distribution , the interval is divided into equally long partial intervals of the length . The mid-point of the interval is the value for .

If we assume that is the inverse function of the standard normal distribution, then the equation

for

generates standard normally-distributed numbers sorted according to size.

A property of these numbers is that they divide the density function of the -distribution into equally-large areas of the size , that is

,

where is the density function of the standard normal distribution.

With a permutation , which can be simulated by drawing -times from the number set without laying back, appropriate random numbers

can be generated.

The advantage of this procedure is that even with a small sample size, the generated sample comes very close to the normal distribution, although this is paid for with longer computation times on account of the inverse function calculation.

Because of the symmetry of the normal distribution , the inverse function of the standard normal distribution only has be calculated -times using an approximation procedure. The remaining values can be specified using the relationship .