I think the most popular alternative to the "normal" Kolmogorow-Smirnow-Test for normal distribution (if the parameters are unknown and therefore have to be estimated) is the Lilliefors-Test. I am thinking about this (maybe too simple) alternative: first, you calculate the empirical mean and empirical variance of the given data (or of a subset of it). Afterwards, you generate a sample of normally distributed random variables with these estimated parameters. Then, you can test, whether the original sample and the generated sample have the same distribution using the 2-sample-kolmogorow-smirnow-test.

This would be a simple method to check, whether a given sample follows a normal distribution. I don't see problems but it seems to be too simple. Does anybody see problems/mistakes in this idea?

Thank you very much!


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.