Hi,
I'm not a statistician so sorry for possible trivial questions ...
I want to perform a GoF test on sample data against several distribution
(like Extreme Value, Phase Type, Pareto, ...).
Since I suspect a long-tailed behaviour on data I want to use
Anderson-Darling (AD) GoF test because it's well known it's more
sensible to tail data.
Looking at R packages the only AD test is the AD normality test
("ad.test") in the "nortest" package. So I think this
function is not
for me since long-tailed samples aren't normally distribuited (right?!)
I've found the Marsaglia article ("Evaluating the Anderson Darling
distribution") where it seems I can consider the ECDF (empirical CDF)
and the theoretical as a uniformly [0,1] distributed data and then
perform the test like I had to compare two uniform distribution. The
problem is the theoretical CDF ( i.e. the parameters of theoretical
distribution) has been estimated from the data against which I want to
make the test. I've read somewhere it's not a good technique to compare
the distribution with the above way because the resulting AD test might
be biased.
So, finally, I don't know how to proceed ...
Can anyone give me a help or any reference (please remember I'm not a
statistician so do not write too technically)??
Thanks a lot to everyone!!
-- Marco
