# Simulating a Normal Process from Sums of Uniform Distributions

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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.

[more]
Contributed by: Jim Gerdy (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Apart from the parameter for the number of uniform distributions to be summed (the slider), you can control the discretization of the distribution and the sample size of the simulation. The uniform distribution is discrete in all cases in this simulation on a grid with points for a few choices of . The sample size varies between 10 and 5000 points.

The statistics of distributions that are the sums of elementary distributions is detailed in most statistics textbooks. For example:

A. M. Mood, F. A. Graybill, and D. C. Boes, *Introduction to the Theory of Statistics*, New York: McGraw-Hill, 1974.