Zipf-Mandelbrot Law

Zipf-Mandelbrot: f(k) ∝ 1/(k+q)^s. Pure Zipf has q=0, s≈1 (word frequencies, city sizes, etc.). Mandelbrot's shift q accounts for the "warm-up" at small ranks. Log-log plot shows power-law as a straight line. Real English word frequencies (top 20 shown in bar): "the"≈7%, "of"≈3.5%, "and"≈2.9%...