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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.

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  • $\begingroup$ 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. $\endgroup$ May 26, 2020 at 19:40
  • $\begingroup$ 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. $\endgroup$
    – dimitriy
    May 26, 2020 at 19:53
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    $\begingroup$ Reminds me of this question, you'll maybe find something interesting in the discussion : stats.stackexchange.com/questions/449359/… $\endgroup$ May 27, 2020 at 7:58

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