 Kolmogorov-Smirnov confidence band

For independent observations from a continuous distribution function, the probability integral transform makes the Kolmogorov-Smirnov statistic distribution-free. Choose $c_{n,\alpha }$ from its uniform-sample distribution to have probability $1-\alpha$ of not exceeding that critical value. Clipping the empirical distribution plus/minus this value to the unit interval gives simultaneous coverage at every argument. This is a band for the entire distribution, rather than separate pointwise intervals.

// Target: statistical-modelling.bigb