curvewise intervals

A pointwise interval contains a proportion of sampled values at each . A curvewise interval contains a proportion of complete sampled curves across every .

Suppose there are sampled curves .

pointwise percentile interval

An 80% pointwise interval uses the 10th and 90th percentiles:

Different curves can determine the boundaries at each . The interval gives 80% coverage for a fixed , but does not generally contain 80% of complete curves.

curvewise interval

ggdist::curve_interval() assigns each complete curve a depth . The deepest curve stays most central relative to the other curves across . The central curve is the deepest sampled curve:

The central line is therefore one actual sampled curve.

The band boundaries generally are not: although each boundary value comes from a selected curve, the curve supplying that value can change with . For a depth cutoff , select

and construct an envelope from the selected curves:

The cutoff is chosen so that approximately 80% of complete curves remain inside the envelope for every :

As the requested width decreases, less central curves are removed. With a unique deepest curve, the smallest envelope collapses to

Use pointwise intervals for uncertainty at a particular . Use curvewise intervals for uncertainty about the complete shape, peak or timing of a curve.