Rank error as a fraction of the tail it is about

Rank error as a fraction of the tail it is about

The same measurements as a plate reporting error against the stream, divided by the mass the quantile is about — 1 − q, which is a half at the median and a thousandth at q = 0.999. Averaged over 8 independent streams of 40,000 Pareto values. A relative promise is a flat line on this plate and an absolute one climbs, because the numerator is constant and the denominator is shrinking. Greenwald–Khanna: 0.64% → 1.37% → 3.63% → 47% → 100%; high-biased: 0.46% → 0.42% → 0.44% → 0.56% → 0.00%; t-digest: 0.33% → 0.50% → 1.15% → 11% → 56%. The vertical axis is logarithmic.

Drawn at 700 × 420, wide on the page. Everything above is what tail-error returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

3 essays call tail-error. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about — which is what optcheck and figfill exist to catch.