Using MATLAB's chi2gof with non-standard user-specified PDFs

Question

I would like to use MATLAB's chi2gof to perform a chi-square goodness-of-fit test. My problem is that my assumed (i.e., theoretical) distribution is not one of the standard built-in probability distributions in MATLAB. The specific form of my desired distribution is:

p = x^a*exp(-b*x^2)

where a and b are constants. There must be a way to use chi2gof for arbitrary PDFs? I have done an exhaustive Google search, but have come up empty-handed.

Answer 1

You can specify a handle to a function that takes a single argument to chi2gof this way:

a = ...
b = ...
c = ...
F = @(x)a*exp(-b*x-c*x.^2); % Technically this is an anonymous function
[H,P,STATS] = chi2gof(data,'cdf',F)

Or in special cases:

a = ...
b = ...
c = ...
F = @(x,a,b,c)a*exp(-b*x-c*x.^2);
[H,P,STATS] = chi2gof(data,'cdf',{F,a,b,c})

the last line of which is equivalent to

[H,P,STATS] = chi2gof(data,'cdf',@(x)F(x,a,b,c))

If the parameters a, b, and c are estimated (e.g., using some fitting process), then you should specify the number of estimated parameters to chi2gof. In this case:

[H,P, STATS] = chi2gof(data,'cdf',F,'nparams',3)

Please read the documentation to learn about the other options.