multiple populations in a single pole

I have histograms that most likely represent multiple populations.

If they distribute normally I know I can use curve fitting to fit a gaussian series.

Is there a way to resolve this with other distributions like weibull, or gamma?

[Rik]

It sounds like there should be.

What is an option as always is finding a direct formula and fitting that. (and of course 'direct' can be quite a broad term in this context)

[TADA]

Yes like the gaussian fitting for normal distribution...

I was hoping for something more user friendly than hours and hours of digging in Wikipedia and articles and praying to be struck by lightning :)

[Star Strider]

I am not certain what you are asking. See if the histfit (link) function will do what you want.

[TADA]

@Star Strider thank you for your comment.

I actualy know of histfit, I know it uses fitdist, which as far as I can tell from trying to figure out the code and from the documentation doesn't fit distributions with more than one populations

here's what I mean:

The top panel shows a histogram of a mocked measurement (I can't disclose real data in this particular case) which has two distinct populations.

The two bottom panels show the histograms of each population separately.

I used here beta distribution to generate the data with no particular reason, it could be anything else. here's the code for that:

rng default; 
b(:,1) = betarnd(3,10,1000,1);
b(:,2) = betarnd(10,4,1000,1);

ax(1) = subplot(2,2,1:2);

histogram(b(:));

hold on;

h = histfit(b(:,1), 15, 'beta');
delete(h(1));

ax(2) = subplot(2,2,3);
h = histfit(b(:,1), 15, 'beta');

ax(1) = subplot(ax(1));
h = histfit(b(:,2), 15, 'beta');
delete(h(1));

ax(3) = subplot(2,2,4);
h = histfit(b(:,2), 15, 'beta');

My measurement produces something like the top panel. The real data it is much more subtle naturally, because real life doesn't have the habbit of making things easy :\

So what I'm looking for is a way of fitting the sum of two or more distribution functions to the same dataset, each distribution whould match a peak in the histogram.

kind of like using curve fitting to fit 'gauss2'

specifically I would probably use gamma and weibul distributions.

Is that possible or do I have to fit an exact formula?

any help would be most appreciated

[Walter Roberson]

fittype() has no built in library functions for fitting sum of distributions, unless you want to count sum of sin()

You can construct a custom anonymous function to use.

I am not familiar with the difficulty of fitting the sum of beta functions. I do know that fitting the sum of gaussians is a lot harder to do well than is at first apparent: it is common with sum of gaussians for the initial point to need to be pretty close to the actual parameters in order to not get a wildly different solution than is optimal.

[TADA]

Ok Thank you

[Walter Roberson]

An approach that might be plausible is to run a minimizer with enough parameters for one instance of the distribution to be fit. The objective function would use those parameters to predict values in the distribution along the independent variable, and would subtract those predicted values from the actual. Then run a fitdist() on what is left specifying the model, and getting back parameters. Use these second parameters together with the first to generate predicted sum of distribution, calculate sum of squares residue against actual data, return that as the objective function value.

[TADA]

Can you point me in the right direction for how to address the minimization?

A link to the documentation or a name of a function/class would be perfect