Do Populations Conform to the Law of Anomalous Numbers?

Sandron, Frédéric

doi:10.3917/pope.204.0753

Cited by 10 publications

(9 citation statements)

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“…For more on the history of the normal distribution, see the work of Patel and Read (1982). 3 Creative applications of Benford's Law are found in connection with religious data (Makous, 2011;Mir, 2012), election frauds (Leemann & Bochsler, 2014), population studies (Sandron, 2002), auctions on eBay (Giles, 2007), survey data (Judge & Schechter, 2009), tax data (Nigrini, 1996), economic data (EU) (Michalski & Stoltz, 2013), Libor manipulations (Abrantes-Metz et al, 2012), accounting fraud detection (Nigrini, 1999), and financial reporting (McGuire, Omer, & Sharp, 2011). For a detailed list of useful application of Benford's Law, see Hürlimann (2006).…”

Section: Endnotesmentioning

confidence: 99%

Can Benford's Law explain CEO pay?

Mukherjee

2017

Corporate Governance

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Manuscript Type Empirical Research Question/Issue This study applies the statistical properties of Benford's Law to CEO pay. Benford's “Law” states that in an unbiased dataset, the first digit values are usually unequally allocated when considering the logical expectations of equal distribution. In this study we question whether the striking empirical properties of Benford's Law could be used to analyze the negotiating power and preferences of CEOs. We argue that performance‐based or market‐determined compensations should follow Benford's Law, demonstrating no direct negotiation by the CEOs. Conversely, deviation from Benford's Law could reveal CEO negotiating power or even preference. Research Findings/Insights Our analysis shows that market‐determined “Option Fair Value” (the dollar value of stock options when exercised) conforms closely to Benford's Law, as opposed to “Salary”, which is fully negotiated. “Bonus”, “Option Award”, and “Total Compensation” are generally also largely consistent with Benford's Law, but with some exceptions. We interpret these exceptions as negotiation by the CEOs. Surprisingly, we found that CEOs prefer to be paid in round figure values, especially “5”. We use Benford's Law to study the negotiating powers of CEOs vs. that of other executives. Finally, we compare the negotiating tactics of CEOs before and after SOX and analyze the impact of firm size on their compensation. Theoretical/Academic Implications This study introduces Benford's Law and its applications within the corporate governance literature. Practitioner/Policy Implications This method could be used by academics, industry and regulators to uncover compensation patterns within large business departments and/or organizations or even entire industry segments.

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Section: Endnotesmentioning

confidence: 99%

Can Benford's Law explain CEO pay?

Mukherjee

2017

Corporate Governance

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“…Furthermore, the law represents the only distribution of leading digits invariant under scale and base transformations [8][9][10][11]. Secondly, numerous data sets from diverse fields conform to the law [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. For an exhaustive list refer to [27].…”

Section: Introductionmentioning

confidence: 99%

Benford’s law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions

2014

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“…For a comprehensive information on the numerous data sets which obey Benford's law and its applications across multiple disciplines the reader is referred to "Benford Online Bibliography" [6]. Some examples are the demographic data [7,8], financial data [9][10][11], scientometric data [12][13][14] and scientific data [15][16][17]. Practically Benford's law is used as a statistical sleuth to detect data manipulation.…”

Section: Introductionmentioning

confidence: 99%

The Benford law behavior of the religious activity data

Mir

2014

Physica A: Statistical Mechanics and its Applications

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An important aspect of religious association is that adherents, as part of their religious duty, carry out various activities. One religious group known for keeping the elaborate records of day-to-day activities of its members is the Jehovah's Witnesses (JWs)-a worldwide Christian religious group. We analyze the historical records of the country-wide data associated with twelve different religious activities of JWs to see if there are any patterns in the distribution of the first digits as predicted by Benford's law. This law states that the first digits of numbers in data sets are not uniformly distributed but often, not always, follow a logarithmic distribution such that the numbers beginning with smaller digits appear more frequently than those with larger ones. We find that the data on religious activities like peak publishers, pioneer publishers, baptizations, public meetings, congregations, bible studies, time spent in door-to-door contacts, attendances at the memorial services, total literature and individual magazines distributed, new subscriptions and back-calls received excellently conforms to Benford's law.Comment: 17 pages, 12 figures, 5 tables, 57 reference

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Do Populations Conform to the Law of Anomalous Numbers?

Cited by 10 publications

References 0 publications

Can Benford's Law explain CEO pay?

Can Benford's Law explain CEO pay?

Benford’s law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions

The Benford law behavior of the religious activity data

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