The standard Anderson darling test is used to test the normality of the sample data. The Hypothesis (H0) is that the data is normally distributed and the alternative hypothesis is (H1) the data doesn't come from normal population. I want to test my sample if it comes from a Weibull population. How do we do it in MATLAB?
The answer to your question can be found in: M. A. Stephens (1986). "Tests Based on EDF Statistics". In D'Agostino, R.B. and Stephens, M.A. Goodness-of-Fit Techniques. New York: Marcel Dekker. ISBN 0-8247-7487-6
@Bothum: I do not see what Jamil can accomplish with what you are suggesting. A Weibull distribution can be highly skewed and asymmetric; there is no way - in those cases - that a normal distribution will come even close to fit the data well.
depends on how noisy the data is
A weibull distribution can be highly skewed or not, that depends on the shape parameter. This distribution fits the distribution of wind speeds at most wind farms and its not highly skewed.
If your data has a high element of random noise (which is a normal distribution) then a normal distribution is often an acceptable fit.
If the data has low noise, you can tell by eye if its normal or not.
Well, if the data can be fit very well by a normal distribution, then why would Jamil try to fit a Weibull?!!!
The A-D test is not specific to the Normal distribution. It can be used to test whether a dataset follows any distribution (see http://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test#The_single-sample_test for details). It should be easy to implement in Matlab. Note that the CDF (Phi) in the wiki page would correspond to that of a Weibull in your case
I join Saif Eddin Jabari , The A-D test is not specific to the Normal distribution.
it calcualte the distance between reference cdf F0 under H0 and any other ditribution under H1.
When doing the AD-test one has to consider 2 cases: out-of-sample testing (parameters are already given) and in-sample testing (parameters are estimated from the data sample itself). In either case, the critical value to compare the AD-test statstic W_n^2 with will depend on sample size and confidence level. For the 95%-confidence level we have for Weibull distributions with sample size N=100 and out-of-sample testing a value of approx. 2.48 (to be compared with Anderson Darling 1954 general asymptotic value for N --> infinity of 2.492) and for the in-sample testing a value of 0.77.
Let me know if you need critical values for different sample sizes.
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