##  [Zipf–Mandelbrot Law](/zipf-mandelbrot-law) 

  ##  [Zipf–Mandelbrot Law](https://information.quantumdictionary.io/zipf-mandelbrot-law-0) 

  

 [![Information & Communication Dictionary](/sites/default/files/styles/large/public/2026-01/Information%20%26%20Communication.png.webp?itok=g4emS-T7)](/topic-specific-dictionaries/information-communication)



**Information & Communication Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.