un-mix a pdf

I'm looking to find the 2 representative particle sizes (x-axis) of a particle size distribution (see attached fig). For a single reprentative particle size, I can compute the mean, or median. But, it looks like it is a mixture of two classes, and I'd like to find the "respresentative" particle size of each class. I thought that fitgmdist might help me here, but it looks like that function needs to start from raw values (not a pdf), and I have a pdf only.

In the figure, I think the answer I'm looking for is ~85 mum and 270 mum, the orange and yellow vertical lines. And tips on how to do this "unmixing"?

I'm

Thank you!

[the cyclist]

Can you share the (x,y) data points that make up the concentration curve?

You might be able to fit a non-linear model using fitnlm. I'm not sure, though.

[Rachel Allen]

Thanks, I don't remember exactly which data set I used to make that last image, but here's the data for a new one:

[the cyclist]

I haven't been able to get my idea to use fitnlm to work. :-(

Answer 1

[Steven Lord]

So you want the local peaks? Take a look at the islocalmax function.

[the cyclist]

I don't think it's just peak-finding. If the distribution is a mixture of two gaussians, the modes tend to get shifted closer toward each other than the means of each gaussian. Here is a contrived example where the gaussian means are at -1.1 and 1.1, but the modes look to be around -0.8 and 0.8.

x = -3 : 0.01 : 3;
pdf_L = normpdf(x,-1.1,1);
pdf_R = normpdf(x, 1.1,1);
pdf_sum = pdf_L + pdf_R;

figure
plot(x,pdf_sum)

[Rachel Allen]

Thanks, I think this does illustrate it well. In addition, there are data sets like the figure attached, where it's easy to believe that there is a second peak, but it would be hard to find with a peak-finding function.

Answer 2

[the cyclist]

I was doing a bit of searching on this forum, and I found this question, where @Image Analyst uploaded his Fit Multiple Gaussians code.

That function looks like it will do what you want. I struggled to adapt it to your data, but I'm not sure if I am just doing something silly at the end of a long day. But I think it's worth a look.

Note that that file is a demo that generates simulated data to illustrate the method. You won't need that part. You'll just need to insert your own.