On the Distribution of First Significant Digits

Pinkham, Roger S.

doi:10.1214/aoms/1177704862

Cited by 233 publications

(160 citation statements)

References 9 publications

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“…In the context of the Th eory of Probabilities, authors such as Hill (1995Hill ( ,1996, Pinkham (1961), and Raimi (1969) showed that the NB Law applies in data of a numerical nature that present invariance with regards to scale and that arise in a random nature. Th us, data on fi nancial fl ows have received considerable attention in the literature as apt for applications using the NB Law.…”

Section: The Newcomb-benford Lawmentioning

confidence: 99%

Using the Newcomb-Benford Law as a Deviation Identification Method in Continuous Auditing Environments: A Proposal for Detecting Deviations over Time

Silva

Travassos²,

Costa³

2017

Rev. contab. finanç.

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This paper used the Newcomb-Benford Law (NB Law) to analyze 210,899 contracts issued by sixty management units in two states in the Brazilian Northeast in 2010. In this article we seek to address the following question: What proposal emerges from the need to identify financial deviations over time in terms of NB Law compliance in continuous auditing scenarios? To this end, the goal of the paper is to analyze this compliance with the aim of identifying deviations over time. The analysis focuses on first significant digit distribution. Graphical analysis of observed frequencies and time series of relative discrepancies reveals the formation of typical patterns of divergences from Public Tenders Law (Federal Law n. 8.666/93). From the results obtained, we conclude that time series analysis of NB Law compliance can improve the accuracy of sampling procedures in continuous auditing.

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Section: The Newcomb-benford Lawmentioning

confidence: 99%

Using the Newcomb-Benford Law as a Deviation Identification Method in Continuous Auditing Environments: A Proposal for Detecting Deviations over Time

Silva

Travassos²,

Costa³

2017

Rev. contab. finanç.

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“…In the 1960s, various aspects of the theoretical context of the Newcomb-Benford curiosity are offered by: Pinkham (1961), Adhikari and Sarkar (1968), Duncan (1969), and Raimi (1969). However, Hill (1995Hill ( a, b, 1996 is usually credited with providing the conclusive theoretical support for the Why and Conditional questions posed above.…”

Section: Why Should Eq(1) Work As a General Dfp-generating Process Esmentioning

confidence: 99%

Testing the Mixing Property of the Newcomb-Benford Profile: Implications for the Audit Context

Lusk¹,

Halperin²

2014

IJEF

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Introduction: Circa 1996 Theodore Hill offered a definitive proof that under certain conditions a data generating process is likely to produce observations that follow the Newcomb-Benford Log10 (N-B) first digit profile. The central feature of Hill's proof is the mixing property from which seems to follow base invariance for scale transformations. Further, it has been observed that small datasets are often not part of the N-B profile set. Study Precise: This suggests that, if indeed the mixing process underlies the generation of the N-B profile, that one should be able to take small Non-Conforming base-invariant datasets that are generated by uncorrupted processes and aggregate them to form datasets that conform to the N-B profile. Results: We demonstrate mixing convergence and find a systematic movement from Non-Conformity to Conformity at a transition point on the order of 250 data points. Impact: We suggest the practical importance of the Hill-Mixing result for the certification audit. We have all of these tests, datasets and results coded in a Decision Support System in VBA: Excel™ that is available from the authors free without restriction to its use.

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“…However, Newcomb's findings were forgotten until the American General Electric physicist Frank Benford (1938) Hill (1995) derived the joint distribution of the first and higher-order significant digits: Pinkham (1961) and Hill (1995) proved that Benford's law is base invariant (i.e. the distribution remains unchanged irrespective whether the numbers are expressed in base 2, 4, 8 etc.)…”

Section: What Is Benford's Law?mentioning

confidence: 99%

Does Benford’s Law hold in economic research and forecasting?

Günnel

Tödter

2008

Empirica

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Abstract:First and higher order digits in data sets of natural and socio-economic processes often follow a distribution called Benford's law. This phenomenon has been used in many business and scientific applications, especially in fraud detection for financial data. In this paper, we analyse whether Benford's law holds in economic research and forecasting. First, we examine the distribution of leading digits of regression coefficients and standard errors in research papers, published in Empirica and Applied Economics Letters. Second, we analyse forecasts of GDP growth and CPI inflation in Germany, published in Consensus Forecasts. There are two main findings: The relative frequencies of the first and second digits in economic research are broadly consistent with Benford's law. In sharp contrast, the second digits of Consensus Forecasts exhibit a massive excess of zeros and fives, raising doubts on their information content.

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On the Distribution of First Significant Digits

Cited by 233 publications

References 9 publications

Using the Newcomb-Benford Law as a Deviation Identification Method in Continuous Auditing Environments: A Proposal for Detecting Deviations over Time

Using the Newcomb-Benford Law as a Deviation Identification Method in Continuous Auditing Environments: A Proposal for Detecting Deviations over Time

Testing the Mixing Property of the Newcomb-Benford Profile: Implications for the Audit Context

Does Benford’s Law hold in economic research and forecasting?

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