Benford's Law — First Digit Distribution

In many naturally-occurring datasets, the first significant digit d appears with probability log₁₀(1 + 1/d). This seems impossible — but it falls naturally from scale-invariant distributions.

χ² stat: —
p-value: —
Max dev: —
KL div: —
n = —

Benford's law (Newcomb 1881, Benford 1938): P(first digit = d) = log₁₀(1+1/d). It holds for any distribution that spans several orders of magnitude. Crucially, it is scale-invariant and base-invariant. Used in forensic accounting to detect fabricated data.