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On Characterizations and Tests of Benford’s Law

Author

Listed:
  • Lucio Barabesi
  • Andrea Cerasa
  • Andrea Cerioli
  • Domenico Perrotta

Abstract

Benford’s law defines a probability distribution for patterns of significant digits in real numbers. When the law is expected to hold for genuine observations, deviation from it can be taken as evidence of possible data manipulation. We derive results on a transform of the significand function that provide motivation for new tests of conformance to Benford’s law exploiting its sum-invariance characterization. We also study the connection between sum invariance of the first digit and the corresponding marginal probability distribution. We approximate the exact distribution of the new test statistics through a computationally efficient Monte Carlo algorithm. We investigate the power of our tests under different alternatives and we point out relevant situations in which they are clearly preferable to the available procedures. Finally, we show the application potential of our approach in the context of fraud detection in international trade.

Suggested Citation

  • Lucio Barabesi & Andrea Cerasa & Andrea Cerioli & Domenico Perrotta, 2022. "On Characterizations and Tests of Benford’s Law," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 1887-1903, October.
    • Handle: RePEc:taf:jnlasa:v:117:y:2022:i:540:p:1887-1903
    DOI: 10.1080/01621459.2021.1891927
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