Zipf's Law

Rank-frequency power laws in natural language, cities, earthquakes & wealth

Zipf's law: frequency ∝ 1/rank^α. For English words α≈1.0 (Zipf 1935). George Zipf observed this in word frequencies; it appears across many complex systems. The log-log plot should show a straight line with slope -α. Deviations at the top (hapax legomena) reveal finite-corpus effects.