How to carry out a chi-squared distribution fit?

　　I want to use central chi-squared distribution to fit a set of data (in order to get its degree of freedom, goodness of fit, etc..). However, in the distribution fitting toolbox, there is no options for chi-squared distribution. I wonder how to solve this problem...

Answer 1

[Wayne King]

How about using mle() with the distribution 'gamma' since the chisquare distribution is just a gamma with alpha parameter nu/2 (nu = dof) and beta parameter = 2

r = chi2rnd(2,100,1);
[phat,pci] = mle(r,'distribution','gamma');

Alternatively, you can do:

[h,p] = chi2gof(r,'cdf',@(x)chi2cdf(x,2),'nparams',1);

which gives you a goodness of fit test on whether the data vector is compatible with the chisquare 2-dof distribution in this case.

Note that with:

[h,p] = chi2gof(r,'cdf',@(x)chi2cdf(x,2),'nparams',1);

you do not reject the null hypothesis (h=0), while with

[h,p] = chi2gof(r,'cdf',@(x)chi2cdf(x,5),'nparams',1);

you do (h=1).

Finally, there is the good old qqplot() to visually assess your fit:

pd = ProbDistUnivParam('gamma',[1 2]);
qqplot(r,pd);you do.