Koen Vermeer <[EMAIL PROTECTED]> wrote in message asneph$s5l$[EMAIL PROTECTED]">news:asneph$s5l$[EMAIL PROTECTED]... > Hi, > > I want to test whether a set is drawn from a normal distribution. With a > Kolmogorov-Smirnov test, I can do this for known mean and variance. The > Lilliefors test is essentially the same, but for unknown mean and variance > (thus estimated from the data). > Now, in my case, I have a known mean (zero) and unknown variance, meaning > that my situation is somewhere in between Kolmogorov-Smirnov and > Lilliefors. Is there a separate test for this? I haven't checked the > Lilliefors paper yet, so maybe I am able to partly follow the paper and > come up with a similar result for known mean and unknown variance, but if > someone else has already done it, I'd rather use those results.
I don't know of it being done, but Lilliefors just used simulation. You could do the same if you wanted. (Another possibility: the Lilliefors and the K-S statistics would provide bounds on your p-value. If the p-value was bounded well away from your nominal significance level, would you particularly need to know it exactly?) You may want to look at the Anderson-Darling test. In the goodness of fit book by D'Agostino and Stephens, (I think, or it may have a reference to a paper in which it can be found) they look at the approximate asymptotic distribution of the A-D under estimation of 0, 1 and 2 parameters, if I am remembering correctly (this is going back about 13 years since I looked at it so I may be misremembering some details). The dependence on the original distribution is apparently not strong, so the test is approximately distribution-free. The asymptotics kick in very rapidly (I think they suggest n=3 is sufficient). They give tables that are based on a function of n and the usual A-D statistic. Glen . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
