Fucking just aight <| sep |> I have two 1 Ddiscretized probability distributions . Real world data so there is noise present . The original data sets were large of the order of thousands of data points . note not I ' m not working with original data sets , only histograms normalized to sum to 1 . I want to test to see if they are the same distribution to within some acceptable threshold , and I need to perform the calculation many times so I need a solution that is fast and parallelisable . The current candidates are KolmogorovSmirnov Kuiper AndersonDarling WassersteinWasserstein looks ideal , but it ' s too computationally expensive . The fastest accurate solution seems to be a combination of KS and Kuiper KS tests any change in mean , Kuiper tests everything else . My Question I ' m referencing Numerical Recipes 3 . pdf and I have no idea what the effective number of data points eq 14 . 3 . 10 should be I think N 1 and N 2 are the degrees of freedom of the data sets which I don ' t have because I ' m working with normalised histograms . Or are Ni the number of nonzero bins ? Alternate question Can you even define the degrees of freedom of a distribution ? If not , I ' ll have to assume that N 1 and N 2 are big and that 14 . 3 . 9 is asymptotic