1
$\begingroup$

Previous question

In my previous question (Kolmogorov-Smirnov test - reliability) I misused two-sample KS test for normality testing of one-sample data. I was given an advice that I should use one-sample KS test, also it was recommended to me to use Anderson-Darling test.

Current situation

I use following C++ implementations of Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) tests to check if given cluster has normal distribution or not.

Problems

If i deal with lets say hundreds of points per cluster, AD gives me satisfactory results. Nevertheless, If I have thousands points in my cluster, I receive large values of A-squared from AD that are far away from AD's critical values.

I have read here that AD fails for large number of points and that it is better to use KS. However, I am not sure, if I did something wrong, but KS is equal to 1.0 in almost every case (cross checked in Matlab too).

Example data

Example data are located here. It represents a cluster of gaussian mixture points. I want to test this cluster for normality (and I want to fail in that test for this data). Consequently, I want to split data to sub-clusters, test each sub-cluster again and split again until I end up with "leaf clusters" that are normally distributed.

Improve this question
$\endgroup$
4
  • 1
    $\begingroup$ The algorithm described in the last paragraph will, with rare exceptions, terminate only when each cluster has one or two points: that's about the only way a cluster can look perfectly "normally distributed." If instead you allow for slight deviations from normality it is not appropriate to use the p-value of a hypothesis test for such a measure (except in the very special case when all clusters have the same counts). This leaves you with a bunch of problems but, as of yet, no clearly articulated question. What exactly are you trying to accomplish in the end? $\endgroup$
    – whuber ♦
    May 7, 2014 at 14:56
  • $\begingroup$ I want to endup with intuitive peaks (if we plot the data as histogram). I was thinking about allowing slight deviations from normality, as you said, in order to have some stop criterion - threshold. $\endgroup$
    – Michal
    May 7, 2014 at 15:19
  • $\begingroup$ You seem to be developing your own algorithm to identify a mixture model. That's not easy to do, but there exist several good, well-known approaches and plenty of software. Check out the links to this term on our site. $\endgroup$
    – whuber ♦
    May 7, 2014 at 15:23
  • $\begingroup$ Yes that is true. However, I've already implemented Approximate gaussian mixtures algorithm (stackoverflow.com/questions/22169492/…) which is based on EM. This algorithm works great, nertheless I have to work with bad 1D peaks (lot of noise, large overlaps). AGM in every EM iteration uses convolution criterion to merge clusters that are overlapping significantly. I am trying to develop algorithm which will compete with AGM and it will try to divide cluster that differs from normal distribution at most. $\endgroup$
    – Michal
    May 12, 2014 at 12:19

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.