How do you fit a gamma distribution?

Hi There

How do you fit a gamma distribution to random data while fixing one of the gamma distribution parameters? Lets say we fix the shaping factor k for example and try to find the scaling factor Thetha of the gamma pdf? How is this done in Matlab?

Answer 1

[Tom Lane]

Expanding on what Wayne wrote, you can supply your fixed-parameter version of the gamma distribution to the mle function. Try this:

x = gamrnd(1.1,100,100,1);
ab = gamfit(x)                                 % fit a and b
b = mle(x,'pdf',@(x,b)gampdf(x,1,b),'start',1) % fix a=1

% compare the empirical distribution and two fits
ecdf(x);
xx = linspace(0,max(x));
line(xx,gamcdf(xx,ab(1),ab(2)),'color','r')
line(xx,gamcdf(xx,1,b),'color','c')

[Wayne King]

That was the piece I was missing! thanks Tom

[Bhekisizwe]

Thanks guys, Thanks a lot...this will definately help me...:-)

[GM Fahad Bin Mostafa]

Hi Tom

I want to fit excel data with gamma in matlab. Would you please help me?

Answer 2

[Wayne King]

You can use either mle() with the 'Distribution','gamma'

gamfit()

or fitdist() with 'gamma'. All require the Statistics Toolbox.

     R = gamrnd(5,2,1e3,1);
     gpdf = fitdist(R,'gamma');
     [phat,phatci] = gamfit(R);
     %same as
     [phat,phatci] = mle(R,'Distribution','gamma');

Once you fix one of the parameters, you can create gamma pdfs by varying the other using gampdf and fit that to your data.