# Gaussian Distribution with Specified Mean and Sigma

**QUESTION:** I have to simulate noise in my experiment, so I want
to create arrays with a normal (Gaussian) distribution of random numbers, but with
a specific full width half maximum (FWHM) and mean. Is this also known as the sigma?

** ANSWER:** Sigma is related to FWHM by the equation:

sigma = FWHM / ( 2 * SQRT(2* ALOG(2)) )

This is typically written as:

sigma = FWHM / 2.35

In IDL you can create an array of random numbers in a normal or Gaussian distribution, with a sigma of standard deviation of 1 with the RANDOMN function. For example, to create 1000 random numbers, you type this:

array = RANDOMN(seed, 1000)

The formula for creating a new distribution of number with a new sigma and mean is this:

new_distribution = array * sigma + mean

So if you want a Gaussian distribution with a mean of 50 and a sigma of 3.5, the you simply do this:

sigma = 3.5 mean = 50.0 array = RANDOMN(seed, 1000) new_distribution = array * sigma + mean

A distribution with these characteristics would have a FWHM calculated like this:

fwhm = sigma * ( 2 * SQRT(2* ALOG(2)) )

Copyright © 1997-2003 David W. Fanning

Last Updated 3 January 2003