Benford's law and Theil transform of financial data

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.

23 pages, 3 tables, 52 refs., 8 figures

References in corpus (2)

• Empirical Mantissa Distributions of Pulsars
• First Digit Distribution of Hadron Full Width

Cited by in corpus (8)

• Breakdown of Benford's Law for Birth Data
• Benford's law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions
• Benford's law first significant digit and distribution distances for testing the reliability of financial reports in developing countries
• The Benford law behavior of the religious activity data
• Decomposition of the Inequality of Income Distribution by Income Types - Application for Romania
• First digit law from Laplace transform
• Benford's laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity
• Seasonal Entropy, Diversity and Inequality Measures of Submitted and Accepted Papers Distributions In Peer-Reviewed Journals