Plotting a function with two terms or alternatively a curve of best fit to a histogram

Hello,

I have a data set (H) that I have plotted on a histogram (Hist). The histogram displays a bimodal distribution.

The histogram includes some negative values on the x-axis. The values for the y-axis are not from data I have in my workspace but instead the frequency of my x-vales that was calculated by the histogram function.

I would like to fit a curve to this histogram that has the function :

f = @(A,m,s,H) A(S) * exp(-((H-m(S))/s(S)).^2) + A(S2) * exp(-((H-m(S2))/s(S2)).^2)

Alternatively, any solution that would allow me to fit a curve of best fit to this data would amazing.

I have trawlled all the forums but haven't found a solution that works.

Any help would be greatly appriciated.

[Adam Danz]

You can get the bin heights from the output handle h=histogram(___) or from the histcounts(__) function.

h = histogram(___)
c = h.Values

% OR

c = histcounts(___)

Then get the center of each bin

binCenters = h.BinEdges(2:end) - h.BinWidth/2; 

Now you've got the x and y values to do the fitting.

[Alice Gold]

Thank you for your answer!

I have attempted doing it this way and by then fitting a curve with the curve fitting toolbox after. However, the array created showing the frequencies is 1x40 and my data is 1x1181 and therefore the curve fitting toolbox does not accept them as compatiable X and Y values.

[Adam Danz]

If I understand you correctly, you want the fit the shape of the histogram, not the shape of your raw data. If that's correct, your x values will be binCenters and the y values will be h.Values (or the output to histcounts) as shown in my comment. Note that the shape will be sensitive to the type of binning you're using. Also see this example of Determine Underlying Probability Distribution.

[Alice Gold]

Ohhh I see what you mean - I was only extracting only the y and not the x values from the histogram! This has now worked! Thank you for your help!

[Torsten]

You can't use curve fitting for this kind of problem since the fitting parameters will strongly depend on the bin width.

Although it might be hard statistics for a beginner, you should read about maximum likelihood estimation and use Matlab's "mle" or the tools for which "the cyclist" provided links.

Wikipedia's article about "Probability distribution fitting" is a good starting point.

Answer 1

[the cyclist]

If you have all of the x values, then you should be able to fit using the fitgmdist function, which will find the best fit to multiple gaussians. You won't need to specify your function.

If you have only the bin locations and counts, then you should be able to use the fitnlm function. You will need to specify your function in this case.

Both of these functions are from the Statistics and Machine Learning Toolbox.

[Alice Gold]

Thank you for your response!