# Gaussian distributed random numbers

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arash on 11 Jul 2014
Commented: Ruben Dörfel on 13 Oct 2020
I need to generate a stationary random numbers with gaussian distribution of zero mean and a variance of unity with max value one.
John D'Errico on 11 Jul 2014
As all the people have pointed out, there are questions that you must answer before you really get a valid response.
Is the mean to be zero and the variance 1 AFTER truncation or before?

Star Strider on 11 Jul 2014
The core MATLAB function randn will produce normally-distributed random numbers with zero mean and unity standard deviation.
If you want the numbers to be limited to those <=1, this will work:
q = randn(1,10);
q = q(q<=1);
Star Strider on 11 Jul 2014
For that matter, considering that the Gaussian distribution has infinite support, once truncated, it is no longer Gaussian.
The mean and variance shift can be ‘fixed’ relatively easily though:
q = q/std(q) - mean(q);
It’s still non-Gaussian, but the numbers work.

Ben11 on 11 Jul 2014
What if you generate some random numbers (here 100) with normal distribution, mean of 0 and std dev of 1:
R = normrnd(0,1,1,100);
then divide all by the highest value so that the maximum is 1:
R_norm = R./max(R(:));
Check max:
max(R_norm(:))
ans =
1
##### 2 CommentsShowHide 1 older comment
Ben11 on 11 Jul 2014
Oh shoot you're right

Chris E. on 11 Jul 2014
Edited: Chris E. on 11 Jul 2014
Well a simple Gaussian distribution code can be as follows:
function main()
xo = 0;
yo = 0;
xsigma = 0.01;
ysigma = 0.01;
particle_amount = 100;
xpoints = Gauss(xo,xsigma,particle_amount)
ypoints = Gauss(yo,ysigma,particle_amount)
%needs column vectors
coordinates_x_y = [xpoints ypoints];
function output = Gauss(xo,sigma,PA)
r = sqrt(-2.0.*(sigma^2).*log(rand(PA,1)));
phi = 2.0.*pi.*rand(PA,1);
output = xo+r.*cos(phi);
This produces as many random Gaussian distribution about the center of (x,y)=(0,0) and a sigma of 0.01 with 100 points of data. You can modify where needed. I hope that helps you out!
Ruben Dörfel on 13 Oct 2020
@Jon Thornburg
Gauss seems to be a user defined function. You would have to put
function output = Gauss(xo,sigma,PA)
r = sqrt(-2.0.*(sigma^2).*log(rand(PA,1)));
phi = 2.0.*pi.*rand(PA,1);
output = xo+r.*cos(phi);
into a new script. You should look up how to implement functions in matlab.