Zipf–Mandelbrot Law

A rank–frequency model generalizing Zipf's law by introducing an additive constant q: the frequency f(r) of the item at rank r is approximated by f(r) ∝ 1/(r + q)^{s}, with parameters s>0 (exponent) and q≥0 (shift). It models the empirical curvature often observed at low ranks and provides a flexible two‑parameter fit to word frequencies and other rank‑ordered data.