Fig 2. Summary of distance distribution derivations for standard normal ($\mathcal{N}(0,1)$) and standard uniform ($\mathcal{U}(0,1)$) data.

Asymptotic estimates are given for both standard (Eq 1) and max-min normalized (Eq 58) q-metrics. These estimates are relevant for all $q\in \mathbb{N}$ and p ≫ 1 for which the normality assumption of distances holds.