Benford's Law
Leading digit distributions in naturally occurring data follow a logarithmic law
P(d) = log₁₀(1 + 1/d)
P(1) ≈ 30.1%
P(9) ≈ 4.6%
Dataset
Powers of 2
Fibonacci sequence
Prime numbers
Factorials
Census simulation
Uniform random
Log-normal
Sample size:
5000
Benford's law applies to data spanning multiple orders of magnitude. Uniform random data does NOT follow it — this is used in fraud detection!