Question: It seems the ApproximateTwoSampleKSTest statistic is not as described in other packages or wikipedia.

[johnabs]

Hi,

I couldn't find anything in the other packages that behave similarly. Not necessarily asking for a change in this package, just the reason behind the (at least to me) confusing notation.

When computing the ks.test in R (using RCall to maintain the values of the samples) the statistic corresponds to the point estimate in the Julia output. Whereas the returned KS-statistic from this package is a different number altogether, which according to the source code corresponds to the value of c(\alpha) (the KS statistic * \sqrt((n*m)/(n+m)).

It seems that the x.\delta (aka the point estimate) and the statistic being returned from R are in line with the definition of the KS-statistic: the supremum function evaluated at the difference of the observed CDFs for the two samples. In this case, why is c(\alpha) being returned as the KS-statistic?

Thank you very much for your time, I greatly appreciate any input you're willing to provide on this matter.