Gaussian distributed random numbers

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arash
arash 2014-7-11
评论： Ruben Dörfel 2020-10-13
I need to generate a stationary random numbers with gaussian distribution of zero mean and a variance of unity with max value one.
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John D'Errico
John D'Errico 2014-7-11
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?

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采纳的回答

Star Strider
Star Strider 2014-7-11
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);
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José-Luis
José-Luis 2014-7-11
编辑：José-Luis 2014-7-11
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
Star Strider 2014-7-11
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.

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更多回答（2 个）

Ben11
Ben11 2014-7-11
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
Chris E.
Chris E. 2014-7-11
编辑：Chris E. 2014-7-11
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!
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Jon Thornburg
Jon Thornburg 2020-6-22
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
Ruben Dörfel 2020-10-13
@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.

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