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Benford's law and Theil transform of financial data

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  • Paulette Clippe
  • Marcel Ausloos

Abstract

Among econophysics investigations, studies of religious groups have been of interest. On 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 along 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 Benford's law use, 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.

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Paper provided by arXiv.org in its series Papers with number 1208.5896.

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Date of creation: Aug 2012
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Publication status: Published in Physica A (2012) 6556-6567
Handle: RePEc:arx:papers:1208.5896

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  1. Janusz Miskiewicz & Marcel Ausloos, 2009. "Has the world economy reached its globalization limit?," Papers 0910.3695, arXiv.org.
  2. Iannaccone, Laurence R, 1995. "Risk, Rationality, and Religious Portfolios," Economic Inquiry, Western Economic Association International, vol. 33(2), pages 285-95, April.
  3. Ausloos, Marcel, 2012. "Econophysics of a religious cult: The Antoinists in Belgium [1920–2000]," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3190-3197.
  4. Stauffer, Dietrich, 2004. "Introduction to statistical physics outside physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 1-5.
  5. Bernhard Rauch & Max Göttsche & Gernot Brähler & Stefan Engel, 2011. "Fact and Fiction in EU‐Governmental Economic Data," German Economic Review, Verein für Socialpolitik, vol. 12(3), pages 243-255, 08.
  6. Laurence R. Iannaccone, 1998. "Corrigenda [Introduction to the Economics of Religion]," Journal of Economic Literature, American Economic Association, vol. 36(4), pages 1941-1941, December.
  7. Dorogovtsev, S.N. & Mendes, J.F.F. & Oliveira, J.G., 2006. "Frequency of occurrence of numbers in the World Wide Web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 548-556.
  8. Miśkiewicz, Janusz & Ausloos, Marcel, 2008. "Correlation measure to detect time series distances, whence economy globalization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6584-6594.
  9. Mir, T.A., 2012. "The law of the leading digits and the world religions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 792-798.
  10. Pietronero, L. & Tosatti, E. & Tosatti, V. & Vespignani, A., 2001. "Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 297-304.
  11. George Judge & Laura Schechter, 2009. "Detecting Problems in Survey Data Using Benford’s Law," Journal of Human Resources, University of Wisconsin Press, vol. 44(1).
  12. Laurence R. Iannaccone, 1998. "Introduction to the Economics of Religion," Journal of Economic Literature, American Economic Association, vol. 36(3), pages 1465-1495, September.
  13. Miśkiewicz, Janusz, 2008. "Globalization — Entropy unification through the Theil index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6595-6604.
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Cited by:
  1. 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.
  2. 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.

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