Zipf's Law

An empirical regularity that in many rank–frequency datasets the frequency f(r) of the item ranked r is approximately proportional to 1/r^s, often with s near 1; when plotted on log–log axes this produces an approximately linear relationship—commonly observed for word frequencies, city sizes, and similar measures.

An empirical regularity for rank–frequency relations stating that the frequency f(r) of the rth most common word is approximately proportional to 1/r^s (often with s ≈ 1), producing a heavy‑tailed distribution where few words are very frequent and many are rare.

An empirical regularity observed in large natural-language corpora in which the frequency of a word is approximately inversely proportional to its rank in a frequency-ordered list: f(r) ∝ 1/r for common ranks, with systematic deviations at the highest and lowest ranks. It is an observation about token distribution, not a theoretical necessity.