🔢 Benford's Law

Dataset:

N numbers—

χ² statistic—

p-value—

Max deviation—

✓ Conforms to Benford's Law

Benford (1938)
P(d) = log₁₀(1 + 1/d)
d=1 → 30.1% d=9 → 4.6%
Natural datasets spanning many orders of magnitude follow this distribution. Deviation → possible fraud.

First-digit distribution — observed (bars) vs Benford expected (line)