MATLAB: Separate Drawing of Gaussian Mixture Model

gaussian distributiongaussian mixture modelgmmnormal distributionnormalizationStatistics and Machine Learning Toolbox

I have a 1D data which need to be separated by two .
So I used
    fitgmdist(data,2);
and got
  1. mu
  2. sigma
  3. component proportion
for each of the gaussian distribution.
And here is the graph. (Gray : Data, Blue : psd of GMModel from fitgmdist)
Until here, everything was okay.
So, question.
How can I separate those two gaussian distribution graph?
I tried
  1. Using makedist('Normal') to create each gaussian distribution.
  2. Multiply by each component proportion
  3. Add two distribution up
But somehow I wasn't able to get the same graph overlapping picture above.
Probably I have the wrong concept of "Normalization" or "Gaussian Mixture Model".
Any advise or site to lookup would be grateful.
———————————————————— @Image Analyst: data uploaded. thanks for the advice I'll remember that next time 🙂

Best Answer

You did something like this:
x = [randn(4000,1)/2; 5+2*randn(6000,1)];
f = fitgmdist(x,2);
histogram(x,'Normalization','pdf')
xgrid = linspace(-4,12,1001)';
hold on; plot(xgrid,pdf(f,xgrid),'r-'); hold off
You can duplicate the pdf values by doing something like this:
n1 = makedist('normal',f.mu(1),sqrt(f.Sigma(1)));
n2 = makedist('normal',f.mu(2),sqrt(f.Sigma(2)));
p = f.ComponentProportion;
y = p(1)*pdf(n1,xgrid) + p(2)*pdf(n2,xgrid);
hold on; plot(xgrid,y,'c--'); hold off
One thing to watch out for. In probability and statistics, it's common to write the standard deviation of a univariate normal distribution as the Greek letter sigma. But it's common to write the covariance matrix of a multivariate distribution as capital Sigma. So that's why I used sqrt(Sigma) to create the univariate distributions.
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