Gaussian distributed random numbers

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]

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?

Answer 1

[Star Strider]

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);

[José-Luis]

This will also change the variance.

[John D'Errico]

The issue is with the question. Is the variance of the sample to be one AFTER truncation?

[José-Luis]

I didn't think it through. If you do it like this, the mean will also change, since you are only removing elements from the right tail. John's question remains valid though.

[Star Strider]

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.

Answer 2

[Ben11]

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

[José-Luis]

Then the variance is not one anymore.

[Ben11]

Oh shoot you're right

Answer 3

[Chris E.]

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!

[John D'Errico]

So randn is not sufficient for you? Note that this does not help, as the request was for a truncated Gaussian.

[Jon Thornburg]

This thead is a few years old but I was looking over the example, because I need to do something similar. I was trying the above code. Gauss(xo,xsigma,particle_amount) it pops out the error "Undefined function or variable 'Gauss'."

Gauss was not deifed as a variable and searching matlab documentation cannot find "Gauss" by itself as formated in the above script. Any suggestions?

[Ruben Dörfel]

@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.