test if gamma distribution is appropriate for my data

Hello! I have some data that i want to fit to a gamma distribution and get the goodness of fit. I used the following commands:

gamfit(left_normalized_dds) %result: 2.1297    0.4696 

shape =  2.1297 ;

scale = 0.4696;

xp = linspace(min(left_normalized_dds),max(left_normalized_dds));

%yp = csnormp(xp,mu,v); %obtain gamma pdf

yp = gampdf(xp,shape,scale); 
% Get the information needed for a histogram.

[nu,x] = hist(left_normalized_dds);

% Get the widths of the bins.

h = x(2)-x(1);

% Plot as density histogram 

bar(x,nu/(length(left_normalized_dds)*h),1)

hold on

plot(xp,yp)

hold off

Is there a way to be sure that the gamma distribution really describes these data? (that's what I mean by goodness of fit). Thanks on advance.

Answer 1

[Rodrigo Osuna Orozco]

You can compute the negative log-likelihood of the parameters of your gamma distribution give your data using "gamlike" (https://www.mathworks.com/help/stats/gamlike.html), but this metric in itself won't tell you if a Gamma distribution describes your data. You can get a maximum likelihood fit to your data for a given family of distributions (i.e. find the maximum likelihood estimate of the parameters of a distribution). You can use the one-sample Kolmogorov-Smirnov test "kstest" (https://www.mathworks.com/help/stats/kstest.html) to test wether your data comes from a given distribution; the examples found in the documentation for "kstest" illustrate this very well.