金融数据的Benford定律和Theil变换
Benford's law and Theil transform of financial data
摘要：
在经济物理学研究中，对宗教团体的研究一直很有意义。一方面，本文研究的是19世纪末在比利时出现的安托万主义共同体财务报告。在不同的时间跨度上已经发现了几种生长-衰变机制。然而，人们普遍怀疑教派的财政状况。本着这种精神，安托万主义社区的年度财务报告，收入和支出，在此根据所谓的本福德定律进行审查。后者通常被用作对可能的会计违规行为的测试。另一方面，本福德定律在尺度和基变换下是不变的。因此，作为对这些数据和本福德定律使用的进一步测试，年度财务报告通过一种泰尔变换（即基于对数变换）进行非线性重新映射。所得数据再次沿本福德定律方案进行分析。奇怪的，令人困惑的，功能被看到。然而，需要强调的是，这种非线性变换可以将论证转向更客观的结论。在附录中，一些简短的讨论，为什么原来的Theil映射不应该使用。在第二个附录中，一个不完美的本福德定律的形式，更适合于异常分布，提出。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
