-1
$\begingroup$

What statistical test should I used if I want to test the difference between shapes of distribution? For exapmle, I have two samples and I want to make a statistical test that will determine wheather the distribution shape of one sample is different than the other.

$\endgroup$
1
  • 1
    $\begingroup$ Do you mean shape up to location and scale (e.g. that any two normal distributions have the same shape) or do you mean the precise shape curve (so two different normal distributions would be different) $\endgroup$
    – Glen_b
    Sep 5, 2017 at 13:58

2 Answers 2

2
$\begingroup$

The Kolmogorov-Smirnov test is the standard approach to compare the empirical distributions of two samples. This approach relies on computing the sup norm between the empirical distribution functions. Most statistical packages include functions to perform two-sample KS test.

Other methods make use of the empirical characteristic functions, as discussed in Amengual, Carrasco and Sentana (2017) (http://www.cemfi.es/ftp/wp/1709.pdf).

$\endgroup$
1
$\begingroup$

If you want to determine whether the probability distributions themselves differ, and not whether samples are drawn from the same distribution (which is what the two-sample KS test checks) then your best bet is with kernel mean embeddings. Essentially, you can use characteristic kernels and your samples to implicitly compare the two pdfs themselves (wikipedia, as always, to the rescue: https://en.wikipedia.org/wiki/Kernel_embedding_of_distributions).

In this particular instance, what you'd want is to see whether the inner product between your two distributions is less than some level that you set, I believe.

$\endgroup$

Your Answer

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.