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Updated: Oct 7, 2025

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A Benford's law based method for fraud detection using R Library.

Caio da Silva Azevedo1, Rodrigo Franco Gonçalves2, Vagner Luiz Gava3

  • 1University of São Paulo, Brazil.

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|January 10, 2022
PubMed
Summary

Benford Law analysis can detect anomalies in large datasets. This study applied Benford Law and statistical tests to identify potential fraud in Brazil's Bolsa Familia welfare program data.

Keywords:
Anomaly detectionBenford's lawBolsa familiaSocial welfare programsStatistical antifraud analysis

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Area of Science:

  • Data Science
  • Statistical Analysis
  • Fraud Detection

Background:

  • Benford Law describes the non-uniform distribution of first digits in naturally occurring datasets.
  • Traditional data analysis may not identify subtle anomalies indicative of fraud.
  • Detecting financial irregularities in large-scale social welfare programs is crucial.

Purpose of the Study:

  • To develop and implement a fraud detection method using Benford Law analysis.
  • To apply this method to the Brazilian Bolsa Familia welfare program dataset.
  • To provide an open-source, accessible tool for auditing social welfare programs.

Main Methods:

  • Application of Benford Law analysis on first and first-two digits.
  • Utilized statistical conformity tests: Z-statistics, Mean Absolute Deviation (MAD), and Chi-square (χ2).
  • Incorporated a summation test for detecting excessively large numbers.
  • Analyzed 13,442,529 records from four periods of the Brazilian welfare program.

Main Results:

  • The study successfully implemented Benford Law analysis for fraud detection.
  • The method was applied to a substantial dataset from the Brazilian Bolsa Familia program.
  • The developed R library and datasets are publicly available for practical implementation.

Conclusions:

  • Benford Law analysis, combined with statistical tests, offers a simple, rapid, and effective method for fraud detection.
  • The technique is easily adaptable for auditing other social welfare programs.
  • Open-source implementation enhances accessibility and promotes wider adoption in financial auditing.