> My question is how we can fit a mixture of Gaussian to a distribution, not
> to the data directly. Let's assume that we have got only the distribution,
> we don't have the original data. Then, if we assume the histogram (or pdf)
> is a mixture of Gaussians, how do we estimate the parameters of this
> model? I found several software (.m files) dealing with GMMs (Gaussian
> mixture models), but all of them fit a GMM to the original data, not to
> the distribution itself. Does anybody know how to solve this problem?
> Thanks a lot for your help;
Ali, it would be better if you could get the original data, but here's an
illustration of fitting a function that is a scaled gaussian mixture density
to some (x,y) data having that form.
% define function that computes this density
f = @(p,x) p(1)*(p(2) *normpdf(x,p(3),abs(p(4))) + ...
% define some parameters
% scale proportion mu1 sig1 mu2 sig2
p0 = [ 10 0.6 25 10 60 20];
% generate normal mixture density plus noise
x = linspace(0,100)';
y = f(p0,x) + 0.01*randn(size(x));
% fit to data and overlay on plot
% hint: start with larger sigma values to help iterations succeed
p = nlinfit(x,y,f,[20 .5 30 30 70 30])