Benford's Law: Detecting Fake Financial Data (DataPhilly)

Very brief talk in detecting fake financial data using Benford's Law. Presented at DataPhilly on May 22, 2014.

Transcript

1. Benford's Law Detecting Fake Financial Data DataPhilly May 22, 2014
2. History • 1881 Simon Newcomb (astronomer) • 1938 Frank Benford (physicist) • 1972 Hal Varian (economist) • 1999 Mark Nigrini (accounting)
3. Probability of First Digit 1 2 3 4 5 6 7 8 9 0% 5% 10% 15% 20% 25% 30% 35%
4. Equation Probability of first digit “D 1 ” is given by: P(D 1 ) = log 10 (D 1 +1) – log 10 (D 1 ) Probability of first two digits being “D 1 D 2 ” is: P(D 1 D 2 ) = log 10 (D 1 .D 2 + 0.1) – log 10 (D 1 .D 2 ) = log 10 (D 1 D 2 + 1) – log 10 (D 1 D 2 )
5. Applicability • Positive, naturally-occurring numbers spanning several orders of magnitude without range limitation. • Not applicable: – Lottery (range limited) – Psychologically manipulative prices ($9.99) – Heights of adults measured in feet (doesn't span orders of magnitude).
6. My Proof Map all positive real numbers to the interval [1,10) by converting to scientific notation and ignoring the exponent.
7. My Proof – Scale Invariance
8. My Proof