algo-risk-benford
Benford's Law Analysis
Overview
Benford's Law predicts that in naturally occurring datasets, the leading digit d appears with probability P(d) = log₁₀(1 + 1/d). Digit 1 appears ~30.1% of the time, digit 9 only ~4.6%. Deviations from this distribution may indicate data fabrication or manipulation. Analysis runs in O(n).
When to Use
Trigger conditions:
- Auditing financial data (expenses, invoices, tax returns) for manipulation
- Screening large datasets for data integrity issues
- Detecting fabricated or artificially rounded numbers
When NOT to use:
- For assigned/sequential numbers (zip codes, phone numbers, IDs)
- For datasets with constrained ranges (e.g., human ages, percentages)
- For small datasets (< 500 records — insufficient statistical power)
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