MATLAB: Histogram Fit: Scaling and offset

Question

I have one dimensional data (~12500 entries) with values reaching from ~135 to ~1150, yielding 3 peaks (see attachment).

Now I want to create a histogram showing the data distribution, as well as a fitting curve and a goodness of fit (chi squared) test.

Thus far I got the following:

    load Data.mat   
    bins = round(sqrt(length(Data)));           % Number of bins
    [f, x] = hist(Data,bins);                   % Calculate histogram
    
    pd = fitdist(x','Kernel');                  % Calculate fit
    y = pdf(pd,f);                              % Calculate pdf
    
    
    figure(1)
    dx = diff(x(1:2));
    bar(x, f/sum(f*dx));                        % Normalizing and plotting
    hold on
    
    plot(x,y,'Linewidth',2)                     % Plot fit
    hold off  
    
    [h,p] = chi2gof(x,'CDF',pd,'Alpha',0.05);   % Chi squared test

While my chi2gof test yields expected results (h=0 ; p = 0.9983) my plot doesn't look to well:

The scale of the fitting curve sems to be way off for all 3 peaks. Additionally I'd expect the curve to get a lot closer to 0 for very low and very high values.

Thanks in advance for any suggestions on how to improve/fix my code!

Answer 1

I think there are a couple of problems. Try this:

load Data.mat
bins = round(sqrt(length(Data)));           % Number of bins
[f, x] = hist(Data,bins);                   % Calculate histogram
pd = fitdist(Data,'Kernel','Width',5);      % Calculate fit
y = pdf(pd,x);                              % Calculate pdf of bin values
figure(1)
dx = diff(x(1:2));
bar(x, f/sum(f*dx));                        % Normalizing and plotting
hold on
y = y / sum(y*dx);
plot(x,y,'Linewidth',2)                     % Plot fit
hold off
[h,p] = chi2gof(x,'CDF',pd,'Alpha',0.05);   % Chi squared test