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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)

Abstract

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.

Keywords

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

Notes

Acknowledgements

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).

References

  1. 1.
    Beelen, T., Dohmen, J.: Parameter estimation for a generalized Gaussian distribution. CASA-report, Technische Universiteit Eindhoven (12) (2015)Google Scholar
  2. 2.
    Benford, F.: The law of anomalous numbers. Proc. Am. Philos. Soc. 78(4), 551–572 (1938)zbMATHGoogle Scholar
  3. 3.
    Bhattacharya, S., Kumar, K.: Forensic accounting and Benford’s law. IEEE Signal Process. Mag. 25(2), 150–152 (2008)CrossRefGoogle Scholar
  4. 4.
    Comesana, P., Pérez-González, F.: The optimal attack to histogram-based forensic detectors is simple(x). In: IEEE International Workshop on Information Forensics and Security, pp. 137–142 (2015)Google Scholar
  5. 5.
    Golbeck, J.: Benfords law applies to online social networks. Plos One 10(8) (2015)CrossRefGoogle Scholar
  6. 6.
    Jolion, J.: Images and Benford’s law. J. Math. Imaging Vis. 14(1), 73–81 (2001)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Mohamed, O.M.M., Jaidane-Saidane, M.: Generalized gaussian mixture model. In: Signal Processing Conference, 2009 European, pp. 2273–2277 (2009)Google Scholar
  8. 8.
    Nigrini, M.J.: Benford’s Law: Applications for Forensic Accounting, Auditing, and Fraud Detection. Wiley, Hoboken, NJ, USA (2012)Google Scholar
  9. 9.
    Ortega, A., Frossard, P., Kovačević, J., Moura, J.M.F., Vandergheynst, P.: Graph signal processing: overview, challenges, and applications. Proc. IEEE 106(5), 808–828 (2018)CrossRefGoogle Scholar
  10. 10.
    Pasquini, C., Comesana-Alfaro, P., Perez-Gonzalez, F., Boato, G.: Transportation-theoretic image counterforensics to first significant digit histogram forensics. In: IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 2699–2703 (2014)Google Scholar
  11. 11.
    Pérez-González, F., Heileman, G.L., Abdallah, C.T.: A generalization of Benford’s law and its application to images. In: Proceedings of the European Control Conference, pp. 3613–3619 (2007)Google Scholar
  12. 12.
    Shi, J., Ausloos, M., Zhu, T.: Benfords law first significant digit and distribution distances for testing the reliability of financial reports in developing countries. Physica Stat. Mech. Appl. 492, 878–888 (2018)CrossRefGoogle Scholar

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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