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.

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#### Best Answer

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).

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