Generalized Benford’s Distribution for Data Defined on Irregular Grid

  • Li-Fang Shi
  • Bin YanEmail author
  • Jeng-Shyang Pan
  • Xiao-Hong Sun
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 834)


In forensic analysis, such as forensic auditing, multimedia forensic, and financial fraud detection, the auditor needs to detect data tempering to find clue for possible fraud. First digit distribution such as Benford’s law is proved to be an efficient tool and is used by many auditing companies to preprocess the data before the actual auditing. However, when the range of the data is limited, the first digit distribution usually does not conform to Benford’s law. Using temperature data from a sensor network, we show that if the data can be modeled by a graph signal model, then after the graph Fourier transformation, the distribution of first digits conforms to a generalized Benford’s law. In addition, a graphic model based on historical data provides better fit to the Benford’s model than that based on geodesic distance. This model is evaluated for simulated data and temperature sensor network. This finding may help to build models for forensic analysis of accounting data and sensor network data for fraud detection.


Fraud detection Benford’s law Graph signal Complex network Graph Fourier transform 



This work is supported by Ministry of Education in China (MOE) Projects of Humanities and Social Science (No. 15YJC790087, 18YJAZH110), National Statistics Science Project (No. 2015LZ59).


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Li-Fang Shi
    • 1
  • Bin Yan
    • 2
    Email author
  • Jeng-Shyang Pan
    • 3
  • Xiao-Hong Sun
    • 1
  1. 1.Department of AuditingShandong University of Science and TechnologyQingdaoChina
  2. 2.College of Electronics Communication and PhysicsShandong University of Science and TechnologyQingdaoChina
  3. 3.College of Computer Science and EngineeringShandong University of Science and TechnologyQingdaoChina

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