Do Populations Conform to the Law of Anomalous Numbers?

Sandron, Frédéric

doi:10.2307/3246664

Cited by 15 publications

(10 citation statements)

References 2 publications

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“…Data sets likely to follow Benford's law are those containing naturally occurring values, values resulting from mathematical operations, values without artificial minima and maxima, and/or values covering a wide range. In what has come to be known as Benford analysis, several diverse data sets have been shown to follow the law, including population (Sandron & Hayford ), financial transactions (Nigrini & Mittermaier ), integer sequences (Washington ), and streamflow (Nigrini & Miller ). In accounting, Benford's law is used to detect fraud, as fabricated or randomly generated data would not likely follow the theoretical distribution of first digits (Durtschi et al , Nigrini & Mittermaier ).…”

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confidence: 99%

Conformance of Public Water Use Data to Benford's Law

Sowby¹

2018

Journal AWWA

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Water use data are essential to managing public water systems, but because most of such data in the United States are self-reported, it is difficult to assess their accuracy. Benford's law, which gives the expected frequency of leading digits in numerical data, could serve as one validation tool. This analysis tests whether Benford's law applies to observations of potable water use by US public water systems. Data at system, county, and state levels were examined using the Kolmogorov-Smirnov test and visual inspection. Almost all were found to conform to Benford's law, although statistical power is generally low, and the tests may favor conclusions of conformance. This finding could serve as a quality check for historical water use data as well as projections. In one example application, two sets of data were compared, and the one known to be more accurate more closely matched Benford's law.

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confidence: 99%

Conformance of Public Water Use Data to Benford's Law

Sowby¹

2018

Journal AWWA

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“…It is worthwhile to mention here that F. Benford used population size of U.S. towns as input data to test and examine the accuracy of his observation [1]. Later on, the population of the 198 countries of world have been shown to follow the first digit law [41]. However, being undertaken by the individual governments, the census estimates of the total populations of countries are expected to be reliable.…”

Section: Discussionmentioning

confidence: 99%

The law of the leading digits and the world religions

Mir

2012

Physica A: Statistical Mechanics and its Applications

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“…Although the Benford law is known for many years, its application in biological systems was barely investigated. Benford’s law was found to be applicable to normal growth of human as well as bacterial populations [ 3 , 8 , 9 ]. Costas et al found that the distribution of cell number per colony of a bacterium M. aeruginosa collected from different locations obeys the Benford law [ 9 ].…”

Section: Introductionmentioning

confidence: 99%

Elucidating tissue specific genes using the Benford distribution

et al. 2016

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BackgroundThe RNA-seq technique is applied for the investigation of transcriptional behaviour. The reduction in sequencing costs has led to an unprecedented trove of gene expression data from diverse biological systems. Subsequently, principles from other disciplines such as the Benford law, which can be properly judged only in data-rich systems, can now be examined on this high-throughput transcriptomic information. The Benford law, states that in many count-rich datasets the distribution of the first significant digit is not uniform but rather logarithmic.ResultsAll tested digital gene expression datasets showed a Benford-like distribution when observing an entire gene set. This phenomenon was conserved in development and does not demonstrate tissue specificity. However, when obedience to the Benford law is calculated for individual expressed genes across thousands of cells, genes that best and least adhere to the Benford law are enriched with tissue specific or cell maintenance descriptors, respectively. Surprisingly, a positive correlation was found between the obedience a gene exhibits to the Benford law and its expression level, despite the former being calculated solely according to first digit frequency while totally ignoring the expression value itself. Nevertheless, genes with low expression that exhibit Benford behavior demonstrate tissue specific associations. These observations were extended to predict the likelihood of tissue specificity based on Benford behaviour in a supervised learning approach.ConclusionsThese results demonstrate the applicability and potential predictability of the Benford law for gleaning biological insight from simple count data.Electronic supplementary materialThe online version of this article (doi:10.1186/s12864-016-2921-x) contains supplementary material, which is available to authorized users.

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Do Populations Conform to the Law of Anomalous Numbers?

Cited by 15 publications

References 2 publications

Conformance of Public Water Use Data to Benford's Law

Conformance of Public Water Use Data to Benford's Law

The law of the leading digits and the world religions

Elucidating tissue specific genes using the Benford distribution

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