KSone Distribution

This is the distribution of maximum positive differences between an empirical distribution function, computed from $n$ samples or observations, and a comparison (or target) cumulative distribution function.

Writing $D_n^{+}={\sup }_t\left(F_{empirical,n}(t)-F_{target}(t)\right)$, ksone is the distribution of the $D_n^{+}$ values. (The distribution of $D_n^{-}={\sup }_t\left(F_{target}(t)-F_{empirical,n}(t)\right)$ differences follows the same distribution, so ksone can be used for one-sided tests on either side.)

There is one shape parameter $n$, a positive integer, and the support is $x\in \left[0,1\right]$.

References

• "Kolmogorov-Smirnov test", Wikipedia https://en.wikipedia.org/wiki/Kolmogorov-Smirnov_test

• Birnbaum, Z. W.; Tingey, Fred H. "One-Sided Confidence Contours for Probability Distribution Functions." Ann. Math. Statist. 22 (1951), no. 4, 592--596.

Implementation: scipy.stats.ksone