Benford’s law and Theil transform of financial data

Paulette Clippe and Marcel Ausloos

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 24, 6556-6567

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.

Keywords: Income; Expenses; Religious community; Benford’s laws; Theil map; Time series (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (31)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:24:p:6556-6567

DOI: 10.1016/j.physa.2012.07.063

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