UFO-Report Database Benford's-Law Audit 3D

Benford Audit (3D, live)

Target database size 600

Fabricated-record fraction 0%

Records ingested

–

χ² statistic

–

Critical value (df=8, α=.05)

15.51

Verdict

–

How it works

Benford's Law: in most naturally occurring, multi-order-of-magnitude numeric datasets, the leading digit follows a logarithmic curve rather than a uniform one:

P(d) = log10(1 + 1/d),  d = 1..9
P(1) ≈ 30.1%   P(5) ≈ 7.9%   P(9) ≈ 4.6%

This scene streams simulated UFO-report reference numbers into the database one at a time, growing the green 3D bars live as each leading digit is tallied. Genuine records are drawn from the true Benford distribution by inverse-CDF sampling; fabricated ones are drawn uniformly across digits 1–9. The translucent cyan reference bars behind them never move — they are the theoretical P(d) heights the observed bars should converge to if the feed is honest.

χ² = Σ (Oᵢ − Eᵢ)² / Eᵢ,   Eᵢ = N·P(i)

Target database size — how many records the live feed ingests before stopping (N).
Fabricated-record fraction — the share of incoming records generated by the uniform (non-Benford) process.
χ² statistic — updates every frame; large values mean the growing green bars are diverging from the cyan reference bars faster than sampling noise explains.
Verdict — flips to flagged once χ² crosses the 8-degrees-of-freedom, 95%-confidence critical value of 15.51.

Real-world relevance: this is the same chi-squared Benford audit forensic accountants run on tax filings, election tallies and lab data — a statistical smell test that catches invented numbers without reading a single record by hand.

Observed (live) Theoretical Benford

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UFO-Report Database Benford's-Law Audit — 3D