Benford's law and Theil transform of financial data

TL;DR

This paper examines the financial reports of the Antoinist community using Benford's law and a Theil transformation to detect anomalies and assess data integrity, revealing complex features and discussing methodological implications.

Contribution

It introduces the application of a Theil log-transformation to financial data analyzed with Benford's law, providing new insights into data irregularities and methodological considerations.

Findings

Detection of puzzling features in financial data

Transformation shifts analysis towards objectivity

Discussion on limitations of Theil mapping

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.