comparing generated data to measured data

Question

we have measured data that we managed to determine the distribution type that it follows (Gamma) and its parameters (A,B)

And we generated n samples (10000) from the same distribution with the same parameters and in the same range (between 18.5 and 59) using for loop

for i=1:1:10000
tot=makedist('Gamma','A',11.8919,'B',2.9927);
tot= truncate(tot,18.5,59);
W(i,:) =random(tot,1,1);
end

Then we tried to fit the generated data using:

h1=histfit(W);

After this we tried to plot the Gamma curve to compare the two curves on the same figure uing:

hold on
h2=histfit(W,[],'Gamma');
h2(1).Visible='off';

The problem s the two curves are shifted as in the following figure "Figure 1 is the generated data from the previous code and Figure 2 is without truncating the generated data"

enter image description here

Any one knows why??

Thanks in advance

Answer 1

By default histfit fits a normal probability density function (PDF) on the histogram. I'm not sure what you were actually trying to do, but what you did is:

% fit a normal PDF
h1=histfit(W); % this is equal to h1 = histfit(W,[],'normal');

% fit a gamma PDF
h2=histfit(W,[],'Gamma');

Obviously that will result in different fits because a normal PDF != a gamma PDF. The only thing you see is that for the gamma PDF fits the curve better because you sampled the data from that distribution.

If you want to check whether the data follows a certain distribution you can also use a KS-test. In your case

% check if the data follows the distribution speccified in tot
[h p] = kstest(W,'CDF',tot) 

If the data follows a gamma dist. then h = 0 and p > 0.05, else h = 1 and p < 0.05.

Now some general comments on your code: Please look up preallocation of memory, it will speed up loops greatly. E.g.

W = zeros(10000,1);
for i=1:1:10000
    tot=makedist('Gamma','A',11.8919,'B',2.9927);
    tot= truncate(tot,18.5,59);
    W(i,:) =random(tot,1,1);
end

Also,

tot=makedist('Gamma','A',11.8919,'B',2.9927);
tot= truncate(tot,18.5,59);

is not depending in the loop index and can therefore be moved in front of the loop to speed things up further. It is also good practice to avoid using i as loop variable.

But you can actually skip the whole loop because random() allows to return multiple samples at once:

tot=makedist('Gamma','A',11.8919,'B',2.9927);
tot= truncate(tot,18.5,59);
W =random(tot,10000,1);