I have a vector of data consisting of about 2 million samples that I suspect is a mixture of two gaussian's. I try to fit the data, Data, to a mixture using matlab's fitgmdist.
From histogram:
% histogram counts of X with 1000 bins.
[Yhist, x] = histcounts(Data, 1000, 'normalization', 'pdf');
x = (x(1:end-1) + x(2:end))/2;
Using fitgmdist:
% Increase no. of iterations. default is 100.
opts.MaxIter = 300;
% Ensure that it does all iterations.
opts.TolFun = 0;
GMModel = fitgmdist(Data, 2, 'Options', opts, 'Start', 'plus');
wts = GMModel.ComponentProportion;
mu = GMModel.mu;
sig = sqrt(squeeze(GMModel.Sigma));
Ygmfit = wts(1)*normpdf(x(:), mu(1), sig(1)) + wts(2)*normpdf(x(:), mu(2), sig(2));
Mixture results with fitgmdist: wts = [0.6780, 0.322], mu = [-7.6444, -9.7831], sig = [0.8243, 0.5947]
Next I try using nlinfit:
% Define the callback function for nlinfit.
function y = nmmix(a, x)
a(1:2) = a(1:2)/sum(a);
y = a(1)*normpdf(x(:), a(3), a(5)) + a(2)*normpdf(x(:), a(4), a(6));
end
init_wts = [0.66, 1-0.66];
init_mu = [-7.7, -9.75];
init_sig = [0.5, 0.5];
a = nlinfit(x(:), Yhist(:), @nmmix, [init_wts, init_mu, init_sig]);
wts = a(1:2)/sum(a(1:2));
mu = a(3:4);
sig = a(5:6);
Ynlinfit = wts(1)*normpdf(x(:), mu(1), sig(1)) + wts(2)*normpdf(x(:), mu(2), sig(2));
Mixture results with nlinfit: wts = [0.6349, 0.3651], mu = [-7.6305, -9.6991], sig = [0.6773, 0.6031]
% Plot to compare the results
figure;
hold on
plot(x(:), Yhist, 'b');
plot(x(:), Ygmfit, 'k');
plot(x(:), Ynlinfit, 'r');
It seems to be that the non-linear fit (red curve) is intuitively a better approximation to the histogram (blue curve) than "fitgmdist" (black curve). The results are similar even if I use a finer histogram, say with 100,000 bins.
What can be the source of this discrepancy?
Added later: Of course one would not expect the results to be the same, but I would expect that the visual quality of the two fits would be comparable.
