Simulating a Normal Process from Sums of Uniform Distributions

A convenient simulation of a random normal process comes from a sum of random uniform variables. The probability density function (pdf) of sums of random variables is the convolution of their pdfs. Sums of uniform random variables can be seen to approach a Gaussian distribution.

This simulation compares the pdf resulting from a chosen number of uniform pdfs to a normal distribution. The top plot shows the probabilities for a simulated sample. The bottom graphic is a quantile plot of the sample compared to the normal distribution. For a sum of 12 uniform random variables, the distribution is approximately normal with a standard deviation near 1.