How do i fit the weibull histogram?

Hello to everyone. I'm plotting a histogram of a data I have. This distribution is most similar to the "weibull distribution". When I fit the graph with the histfit command, it does not match the graph. I found the scale and shape values of the weibull distribution with the fitdist command. I tried plotting a manual weibull distribution to fit the histogram, but it still doesn't match the histogram. I will share all the outputs with you. This is the code I wrote to draw it manually. I would be very grateful if you could tell me how to properly fit the histogram.

histfit(signalhist_poz,1000,'weibull');

histogram(signalhist_poz)

fitdist

Weibull distribution

A = 0.141626 [0.140708, 0.14255]

B = 0.652068 [0.649942, 0.654202]

PD=makedist('Weibull','a',0.141626,'b',0.652068)

X = 0:.01:1.2;

pdf_weibull = pdf(PD,X);

histogram(signalhist_poz);

hold on

plot(X,pdf_weibull,'LineWidth',2)

Answer 1

[TADA]

The PDF you calculated should be normalized to the area of the histogram first.

Here's how histfit does it more or less:

pd=makedist('Weibull','a',0.141626,'b',0.652068) ;
n = 1000;
signalhist_poz = PD.random(n, 1);
X = 0:.01:1.2;
pdf_weibull = pdf(PD,X);
nbins = 100;



figure(1);
clf();
h = histogram(signalhist_poz, nbins);
binedges = h.BinEdges;
hold on
plot(X,pdf_weibull,'LineWidth',2);

% Normalize the density to match the total area of the histogram
binwidth = abs(binedges(2)-binedges(1)); % Finds the width of each bin


% this is where the magic happens
area = n * binwidth;
y = area * pdf_weibull;



figure(2);
clf();
histogram(signalhist_poz, 100);
hold on;
plot(X,y,'LineWidth',2)

[studentmatlaber]

Thank you very much for your reply. I got the correct result. If you don't mind, I want to ask a question. I used the following code to calculate mean square error while drawing with histfit.

 h = histfit(signalhist_poz,1000,'weibull');
histdata = get(h(1),'XData');                   % Get Histogram Data
redcurve = get(h(2),'YData');                   % Get Fit Data
histctrs = mean(histdata);                      % Mean Of Bin Edges
redcurve2 = mean(reshape(redcurve, 2, []));     % Mean Of Bin Edges Fit
fit_err = histctrs - redcurve2;                 % Error
SSE = sum(fit_err.^2);                          % Sum-Squared Error
MSE = mean(fit_err.^2);                         % Mean-Squared-Error

What modification do I need to make now to find the mean square error? Thank you again.

[TADA]

I'm not sure. what exactly do you want to achieve? do you want confidence intervals around the fitted distribution?

Its definitely useful to read about probability plots such as this: https://www.mathworks.com/help/stats/wblplot.html

And about residual analysis, maybe start from this: https://www.mathworks.com/help/stats/residuals.html

https://www.mathworks.com/help/curvefit/residual-analysis.html

[TADA]

If this doesn't help, it might be a good idea to post a new question. That way, people may find their answer next time they encounter similar problem, and new people will notice your question, so you can attract the attention of the forum experts

[studentmatlaber]

Thank you very much for your help.