A0329
Title: A generalization of Benford's law that considers relative quantities
Authors: Mario Maggi - University of Pavia (Italy) [presenting]
Roy Cerqueti - Sapienza University of Rome (Italy)
Alex Ely Kossovsky - independent (United States)
Claudio Lupi - University of Molise (Italy)
Abstract: Benford's law is a discrete probability distribution often observed in the significant digits of many datasets. A wide range of natural phenomena and human-derived data exhibit a high frequency of low significant digits. This behavior is commonly described by Benford's law. Deviations from Benford's law may indicate that the data are bounded, non-numerical (such as codes), or manipulated. This latter point makes Benford's law a useful tool for detecting anomalies and fraud. This paper proposes a generalization of Benford's law, which is named the general law of relative quantities (GLORQ). The GLORQ is a two-parameter discrete probability distribution that is independent of the numeral system used. Like Benford's law, which is a special case, the GLORQ considers data bins that repeat and expand over different orders of magnitude. After introducing the theoretical derivation of the GLORQ, some relations between it and power law variables are presented. Some empirical examples are also provided. Moreover, some simulation studies may suggest the usefulness of the GLORQ in detecting some data manipulations that comply with Benford's law.
