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I have two distributions A and B and I am looking for a goodness of fit test that measures how much the tail of A matches (or fail to match) the tail of B. Alternatively, I am looking for a test that gives me goodness of fitting for collection of percentiles or maybe it measures the amount of probability past some fixed value--anyone of these measure would work. Any pointer is very appreciated.

I do not know either of the distributions, I only have samples from both of them.

Steve
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  • Regarding *I need something similar to KS 2 sample test but takes the tails of the distributions into account* (,and similarly, the title): KS test does take into account tails, alongside the non-tail areas. You probably need one that takes *only* the tails into consideration. You may wish to edit the post and its title accordingly. – Richard Hardy May 26 '20 at 19:40
  • Have you considered a simultaneous quantile regression for the tails on a dummy for sample B? You can then test the joint null that all the sample B coefficients are zero. – dimitriy May 26 '20 at 19:53
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    Reminds me of this question, you'll maybe find something interesting in the discussion : https://stats.stackexchange.com/questions/449359/test-which-distribution-has-a-longer-tail/449367#449367 – Camille Gontier May 27 '20 at 07:58

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