How to plot Central/Non-central chi square pdf?

I have 1000 samples of energy. I want to plot central and non-central chi square pdf. I checked the Matlab documentation, I don't understand, how to calculate/choose values of degree of freedom and delta. Can anyone help?

Answer 1

[Jeff Miller]

You need to estimate the distribution parameter(s) from your 1000 data values (call them x).

In principle you would use fitdist(x,'chisquare') or 'noncentralchisquare', but I don't think the matlab distribution-fitter recognizes either of these two distributions.

If you are willing to do some downloading, I think you can do what you want with Cupid .

The commands would look something like this:

mychi=ChiSq(10);  % Make a chi-square distribution object
mychi.EstML(x)    % Estimate its parameter based on your data
xvals = 0.1:.1:20;  % Pick a range of x values over which you want to plot the distribution
pdfvals = mychi.PDF(xvals,);  % Compute the pdf of the distribution at each x value
plot(xvals,pdfvals);  % plot the distribution

mynoncenchi=ChiSqNoncentral(10,.2);  % Same as above, but using a different distribution object.
mynoncenchi.EstML(x)
noncenpdfvals = mynoncenchi.PDF(xvals,);
plot(xvals,noncenpdfvals);

where x is your data, and 10 and .2 are your initial guesses for the distribution parameters.