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Benford’s law and Theil transform of financial data

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  • Clippe, Paulette
  • Ausloos, Marcel

Abstract

Among econophysics investigations, studies of religious groups have been of interest. On the one hand, the present paper concerns the Antoinist community financial reports–a community which appeared at the end of the 19-th century in Belgium. Several growth–decay regimes have been previously found over different time spans. However, there is common suspicion about sect finances. In that spirit, the Antoinist community yearly financial reports, income and expenses, are hereby examined through the so-called Benford’s law. The latter is often used as a test about possible accounting wrongdoings. On the other hand, Benford’s law is known to be invariant under scale and base transformation. Therefore, as a further test, of both such data and the use of Benford’s law, the yearly financial reports are nonlinearly remapped through a sort of Theil transformation, i.e. based on a log-transformation. The resulting data is again analyzed along the Benford’s law scheme. Bizarre, puzzling, features are seen. However, it is emphasized that such a non-linear transformation can shift the argument toward a more objective conclusion. In an appendix, some brief discussion is made on why the original Theil mapping should not be used. In a second appendix, an imperfect Benford’s law-like form–better suited for anomalous distributions–is presented.

Suggested Citation

  • Clippe, Paulette & Ausloos, Marcel, 2012. "Benford’s law and Theil transform of financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6556-6567.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:24:p:6556-6567
    DOI: 10.1016/j.physa.2012.07.063
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    Citations

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    Cited by:

    1. Marcel Ausloos & Rosella Castellano & Roy Cerqueti, 2016. "Regularities and Discrepancies of Credit Default Swaps: a Data Science approach through Benford's Law," Papers 1603.01103, arXiv.org.
    2. Paul Hofmarcher & Kurt Hornik, 2013. "First Significant Digits and the Credit Derivative Market During the Financial Crisis," Contemporary Economics, University of Finance and Management in Warsaw, vol. 7(2), June.
    3. Salois, Matthew J., 2013. "Regional changes in the distribution of foreign aid: An entropy approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2893-2902.
    4. Jing Shi & Marcel Ausloos & Tingting Zhu, 2017. "Benford's law first significant digit and distribution distances for testing the reliability of financial reports in developing countries," Papers 1712.00131, arXiv.org.
    5. Carrera, César, 2014. "Tracking the Exchange Rate Management in Latin America," Working Papers 2014-020, Banco Central de Reserva del Perú.
    6. Marcel Ausloos & Roy Cerqueti, 2016. "Studies on Regional Wealth Inequalities: the case of Italy," Papers 1602.05356, arXiv.org.
    7. Alexandre Donizeti Alves & Horacio Hideki Yanasse & Nei Yoshihiro Soma, 2016. "An analysis of bibliometric indicators to JCR according to Benford’s law," Scientometrics, Springer;Akadémiai Kiadó, vol. 107(3), pages 1489-1499, June.
    8. Ausloos, Marcel & Jovanovic, Franck & Schinckus, Christophe, 2016. "On the “usual” misunderstandings between econophysics and finance: Some clarifications on modelling approaches and efficient market hypothesis," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 7-14.
    9. Roy Cerqueti & Marcel Ausloos, 2015. "Statistical assessment of regional wealth inequalities: the Italian case," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(6), pages 2307-2323, November.
    10. Marcel Ausloos & Roy Cerqueti & Tariq A. Mir, 2017. "Data science for assessing possible tax income manipulation: The case of Italy," Papers 1709.02129, arXiv.org.
    11. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    12. Ausloos, M. & Herteliu, C. & Ileanu, B., 2015. "Breakdown of Benford’s law for birth data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 736-745.
    13. Mir, T.A., 2014. "The Benford law behavior of the religious activity data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 1-9.
    14. Tariq Ahmad Mir & Marcel Ausloos & Roy Cerqueti, 2014. "Benford's law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions," Papers 1410.2890, arXiv.org.
    15. Carrera, César, 2015. "Tracking exchange rate management in Latin America," Review of Financial Economics, Elsevier, vol. 25(C), pages 35-41.
    16. Ausloos, Marcel & Cerqueti, Roy & Lupi, Claudio, 2017. "Long-range properties and data validity for hydrogeological time series: The case of the Paglia river," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 39-50.
    17. Tudorel Andrei & Bogdan Oancea & Peter Richmond & Gurjeet Dhesi & Claudiu Herteliu, 2017. "Decomposition of the Inequality of Income Distribution by Income Types - Application for Romania," Papers 1709.07960, arXiv.org.
    18. Roy Cerqueti & Marcel Ausloos, 2014. "Assessing the Inequalities of Wealth in Regions: the Italian Case," Papers 1410.4922, arXiv.org.
    19. McCartney, Mark & Glass, David H., 2015. "A three-state dynamical model for religious affiliation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 145-152.

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