The law of the leading digits and the world religions

Mir, Tariq Ahmad

doi:10.1016/j.physa.2011.09.001

Cited by 39 publications

(30 citation statements)

References 28 publications

(30 reference statements)

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“…Benford’s Law has been extensively applied to a wide variety of natural and man-made data sets, such as numerical data on the country-wise adherent distribution of major world religions (Mir 2012), financial data of religious community (Clippe and Ausloos 2012), fraud detection in scientific publications (Hein et al 2012), detecting electoral fraud (Beber and Scacco 2012), time series analysis of seismic clusters (Sottili et al 2012), experimental values of β -decay half-lives (Ni et al 2009) and hydrological data (Nigrini and Miller 2007). …”

Section: Introductionmentioning

confidence: 99%

Benford’s Law and articles of scientific journals: comparison of JCR® and Scopus data

2013

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Benford’s Law is a logarithmic probability distribution function used to predict the distribution of the first significant digits in numerical data. This paper presents the results of a study of the distribution of the first significant digits of the number of articles published of journals indexed in the JCR® Sciences and Social Sciences Editions from 2007 to 2011. The data of these journals were also analyzed by the country of origin and the journal’s category. Results considering the number of articles published informed by Scopus are also presented. Comparing the results we observe that there is a significant difference in the data informed in the two databases.

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Section: Introductionmentioning

confidence: 99%

Benford’s Law and articles of scientific journals: comparison of JCR® and Scopus data

2013

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“…In a randomly distributed unbiased dataset of stock prices, for example, "1" is the first digit almost 30.1 percent of the time, whereas "9" occurs only 5 percent of the time (Corazza, Ellero, & Zorzi, 2010;Ley, 1996). This statistical phenomenon has been found in all unbiased datasets; studies have confirmed its existence on the basis of data from disparate fields (Abrantes-Metz, Kraten, Metz, & Seow, 2012;Benford, 1938;Leemann & Bochsler, 2014;Mir, 2012;Nigrini, 1996;Nigrini & Mittermaier, 1997). Although there is no universal mathematical explanation for this phenomenon, which is no different from the "bell curve" of normal distribution, its empirical validity is too striking to ignore (Patel & Read, 1982;Raimi, 1976).…”

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confidence: 90%

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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“…Under the 95% confidence level, the value of χ 2 is χ 2 (8) = 15.51, which is the critical value for acceptance or rejection of H 0 . If the value of the calculated χ 2 is less than the critical value then the null hypothesis is accepted and concludes that the data fits Benford's law [43,44].…”

Section: First Digit Distribution and Significance Testmentioning

confidence: 99%

Quantifying non-stationarity effects on organization of atmospheric turbulent eddy motion by Benford's law

2016

Communications in Nonlinear Science and Numerical Simulation

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The law of the leading digits and the world religions

Cited by 39 publications

References 28 publications

Benford’s Law and articles of scientific journals: comparison of JCR® and Scopus data

Benford’s Law and articles of scientific journals: comparison of JCR® and Scopus data

Can Benford's Law explain CEO pay?

Quantifying non-stationarity effects on organization of atmospheric turbulent eddy motion by Benford's law

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