Re: fit F distribution

I tried with my own data though and tried many different starting values
but the following error kept coming up:

?? Error using ==> mlecustom>llf_pdfcdf at 431
The PDF function returned NaN or infinite values.

Leo, your variable has mean 3.1338 and variance 4.5367. There's no F
distribution with those values. To get a mean of about 3 you'd need your
second parameter to be 3, and the variance is infinite in that case. This
doesn't prove there's no maximum likelihood estimate, but I can imagine the
mle function might run into trouble trying parameter values that approach
the boundary of the parameter space or for some other reason cause trouble.

I also tried Peter's idea, but didn't wind up with an F distribution.

Is there a theoretical or other reason you need an F distribution? For no
good reason I picked the value 3 and was able to fit x/3 by an F
distribution reasonably well:

ecdf(x)
p = mle(x/3,'pdf',@fpdf,'start',1:2)
p =
9.7097 18.9723
xx = linspace(0,14); line(xx,fcdf(xx/3,p(1),p(2)),'color','r')

I can even estimate the scale parameter:

q = mle(x,'pdf',@(x,v1,v2,s) (1./s) .* fpdf(x/s,v1,v2),'start',[10 10 3])
q =
47.4769 7.9663 2.3680
line(xx,fcdf(xx/q(3),q(1),q(2)),'color','m')

-- Tom


.

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