= Kolmogorov-Smirnov confidence band
{c}
{title2=$[\max(0,\widehat F_n-c_{n,\alpha}),\min(1,\widehat F_n+c_{n,\alpha})]$}
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
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