Kolmogorov–Smirnov Two-Sample Test

The KS test compares two whole distributions, not just their means. The statistic D is the largest vertical gap between the two empirical CDFs.

Implement:

• ecdf(sample, x): the fraction of the sample <= x, for each value in x
• ks_statistic(a, b): D, evaluated at every value in the pooled sample
• ks_pvalue(D, n, m): the asymptotic p-value. With $n_e = \frac{nm}{n + m}$ and $\lambda = (\sqrt{n_e} + 0.12 + 0.11/\sqrt{n_e})\,D$, it's $Q(\lambda) = 2\sum_{k=1}^{100}(-1)^{k-1}e^{-2k^2\lambda^2}$, clipped to [0, 1]
• ks_test(a, b): (D, p)