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