Using Benford’s law on the seismic reflectivity analysis

2018 ◽  
Vol 6 (3) ◽  
pp. T689-T697
Author(s):  
Isadora A. S. de Macedo ◽  
Jose Jadsom S. de Figueiredo
Keyword(s):  
Geomagnetic Field ◽  
Point Of View ◽  
P Wave ◽  
Benford’S Law ◽  
Common Procedure ◽  
Data Set ◽  
Benford's Law ◽  
Distribution Point ◽  
Seismic Reflectivity ◽  
Reflectivity Data

Benford’s law (BL) is a mathematical theory of leading digits. This law predicts that the distribution of first digits of real-world observations is not uniform and follows a trend in which measurements with a lower first digit (1, 2, …) occur more frequently than those with higher first digits (…, 8, 9). A data set from earth’s geomagnetic field, the estimated time in years between reversals of earth’s geomagnetic field, the seismic P-wave speed of earth’s mantle below the southwest Pacific, and other geophysical data obey the BL. Although there are other statistical methods for analyzing a data set, we test, for the first time, the analysis of the seismic reflectivity through the Benford distribution point of view. We applied the BL on real reflectivity data from two wells from the Penobscot field and another two from the Viking Graben field. In both data sets, the reflectivity was in conformity with the BL. Moreover, after analyzing the effect of sonic and density logs despiking on Benford’s distribution through the BL, we found an optimum coefficient for the despiking process, which was a common procedure used to edit the well-log data before its use on reservoir studies.

scholarly journals THE LINK BETWEEN EARNINGS MANAGEMENT AND DIGITAL PATTERN / O elo entre gerenciamento de resultado e padrão digital

2014 ◽  
Vol 14 (1) ◽  
pp. 351
Author(s):  
Jennifer Martínez Ferrero ◽  
Beatriz Cuadrado Ballesteros ◽  
Marco Antonio Figueiredo Milani Filho
Keyword(s):  
Earnings Management ◽  
Financial Reporting ◽  
Reporting Quality ◽  
Poor Quality ◽  
Financial Data ◽  
Benford’S Law ◽  
Similar Distribution ◽  
Data Set ◽  
Benford's Law ◽  
High Degree

<p>According to Dechow and Dichev (2002) and Lin and Wu (2014), a high degree of earnings management (EM) is associated with a poor quality of information. In this sense, it is possible to assume that the financial data of companies that manage earnings can present different patterns from those with low degree of EM. The aim of this exploratory study is to test whether a financial data set (operating expenses) of companies with high degree of EM presents bias. For this analysis, we used the model of Kothari and the modified model of Jones (“Dechow model” hereafter) to estimate the degree of EM, and we used the logarithmic distribution of data predicted by the Benford’s Law to detect abnormal patterns of digits in number sets. The sample was composed of 845 international listed non-financial companies for the year 2010. To analyze the discrepancies between the actual and expected frequencies of the significant-digit, two statistics were calculated: Z-test and Pearson’s chi-square test. The results show that, with a confidence level of 90%, the companies with a high degree of EM according to the Kothari model presented similar distribution to that one predicted by the Benford’s Law, suggesting that, in a preliminary analysis, their financial data are free from bias. On the other hand, the data set of the organizations that manage earnings according to the Dechow model presented abnormal patterns. The Benford´s Law has been implemented to successfully detect manipulated data. These results offer insights into the interactions between EM and patterns of financial data, and stimulate new comparative studies about the accuracy of models to estimate EM.</p><p>Keywords:<strong> </strong>Earnings management (EM). Financial Reporting Quality (FRQ). Benford’s Law.</p>

scholarly journals Benford’s Law as an Instrument for Fraud Detection in Surveys Using the Data of the Socio-Economic Panel (SOEP)

2011 ◽  
Vol 231 (5-6) ◽  
Author(s):  
Jörg-Peter Schräpler
Keyword(s):  
Probability Function ◽  
Fraud Detection ◽  
Numerical Data ◽  
Benford’S Law ◽  
Continuous Data ◽  
Data Set ◽  
Benford's Law ◽  
User Data

SummaryThis paper focuses on fraud detection in surveys using Socio-Economic Panel (SOEP) data as an example for testing newly methods proposed here. A statistical theorem referred to as Benford’s Law states that in many sets of numerical data, the significant digits are not uniformly distributed, as one might expect, but adhere to a certain logarithmic probability function. In order to detect fraud, we derive several requirements that should, according to this law, be fulfilled in the case of survey data.We show that in several SOEP subsamples, Benford’s Law holds for the available continuous data. For this analysis, we developed a measure that reflects the plausibility of the digit distribution in interviewer clusters. We are thus able to demonstrate that several interviews that were known to have been fabricated and therefore deleted in the original user data set can now be detected using this method. Furthermore, in one subsample, we use this method to identify a case of an interviewer falsifying ten interviews not previously detected by the fieldwork organization.

scholarly journals A local Benford Law for a class of arithmetic sequences

2019 ◽  
Vol 15 (03) ◽  
pp. 613-638
Author(s):  
Zhaodong Cai ◽  
A. J. Hildebrand ◽  
Junxian Li
Keyword(s):  
Large Class ◽  
Local Level ◽  
Fibonacci Numbers ◽  
Point Of View ◽  
Benford’S Law ◽  
Local Distribution ◽  
Local Point ◽  
Arithmetic Sequences ◽  
Benford's Law ◽  
Benford Law

It is well known that sequences such as the Fibonacci numbers and the factorials satisfy Benford’s Law; that is, leading digits in these sequences occur with frequencies given by [Formula: see text], [Formula: see text]. In this paper, we investigate leading digit distributions of arithmetic sequences from a local point of view. We call a sequence locally Benford distributed of order [Formula: see text] if, roughly speaking, [Formula: see text]-tuples of consecutive leading digits behave like [Formula: see text] independent Benford-distributed digits. This notion refines that of a Benford distributed sequence, and it provides a way to quantify the extent to which the Benford distribution persists at the local level. Surprisingly, most sequences known to satisfy Benford’s Law have rather poor local distribution properties. In our main result we establish, for a large class of arithmetic sequences, a “best-possible” local Benford Law; that is, we determine the maximal value [Formula: see text] such that the sequence is locally Benford distributed of order [Formula: see text]. The result applies, in particular, to sequences of the form [Formula: see text], [Formula: see text], and [Formula: see text], as well as the sequence of factorials [Formula: see text] and similar iterated product sequences.

Data Diagnostics Using Second-Order Tests of Benford's Law

2009 ◽  
Vol 28 (2) ◽  
pp. 305-324 ◽  
Author(s):  
Mark J. Nigrini ◽  
Steven J. Miller
Keyword(s):  
Numerical Data ◽  
Second Order ◽  
Benford’S Law ◽  
Data Sets ◽  
Data Set ◽  
Accounting Data ◽  
Benford's Law ◽  
Rounded Data ◽  
Analytical Procedures ◽  
Digit Frequencies

SUMMARY: Auditors are required to use analytical procedures to identify the existence of unusual transactions, events, and trends. Benford's Law gives the expected patterns of the digits in numerical data, and has been advocated as a test for the authenticity and reliability of transaction level accounting data. This paper describes a new second-order test that calculates the digit frequencies of the differences between the ordered (ranked) values in a data set. These digit frequencies approximate the frequencies of Benford's Law for most data sets. The second-order test is applied to four sets of transactional data. The second-order test detected errors in data downloads, rounded data, data generated by statistical procedures, and the inaccurate ordering of data. The test can be applied to any data set and nonconformity usually signals an unusual issue related to data integrity that might not have been easily detectable using traditional analytical procedures.

Act natural, because of Benford’s Law

2020 ◽  
pp. 49-52
Author(s):  
Susan D'Agostino
Keyword(s):  
Stock Prices ◽  
Large Data ◽  
Benford’S Law ◽  
Data Sets ◽  
Mathematics Students ◽  
Data Set ◽  
Subsequent Investigation ◽  
Benford's Law ◽  
Tax Returns ◽  
Population Counts

“Act natural, because of Benford’s Law” explains how and why large data sets generated as a result of human behavior concerning health records, population counts, tax returns, stock prices, national debts, election data, and more, have numbers whose first digits are unevenly distributed, with Benford’s Law offering percentages. When an individual tampers with a naturally generated data set, they often introduce fake numbers whose first digits are (more or less) evenly distributed from one to nine. Often, a subsequent investigation reveals that someone has tampered with the data set. Mathematics students and enthusiasts are encouraged to act natural so as to avoid looking like a fraudulent data set that does not observe Benford’s Law. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

Benfordʼs Law in the Natural Sciences

Benford's Law ◽  
2015 ◽  
Author(s):  
David Hoyle
Keyword(s):  
Scale Invariance ◽  
Natural Sciences ◽  
Scientific Data ◽  
Benford’S Law ◽  
Reasonable Assumption ◽  
Data Sets ◽  
Scale Invariant ◽  
Data Set ◽  
Benford's Law ◽  
Potential Applications

This chapter focuses on the occurrence of Benford's law within the natural sciences, emphasizing that Benford's law is to be expected within many scientific data sets. This is a consequence of the reasonable assumption that a particular scientific process is scale invariant, or nearly scale invariant. The chapter reviews previous work from many fields showing a number of data sets that conform to Benford's law. In each case the underlying scale invariance, or mechanism that leads to scale invariance, is identified. Having established that Benford's law is to be expected for many data sets in the natural sciences, the second half of the chapter highlights generic potential applications of Benford's law. Finally, direct applications of Benford's law are highlighted, whereby the Benford distribution is used in a constructive way rather than simply assessing an already existing data set.

Benfordʼs Law as a Bridge between Statistics and Accounting

Benford's Law ◽  
2015 ◽  
Author(s):  
Richard J. Cleary ◽  
Jay C. Thibodeau
Keyword(s):  
Statistics Education ◽  
Point Of View ◽  
Accounting Students ◽  
Benford’S Law ◽  
Statistical Point ◽  
Accounting Practice ◽  
Current State ◽  
Key Concepts ◽  
Benford's Law

This chapter explores the connections between statistics and accounting through Benford's law and considers the questions of when and how to effectively deliver this material in such a way that Benford's law can be a tool that helps accountants make stronger and more efficient decisions using sound statistical practice. It looks at the current state of statistics education for accounting students and presents some of the ways in which accounting practice, particularly in auditing, can benefit from a statistical point of view. The chapter then demonstrates how Benford's law can be used to reinforce the key concepts that appear at the intersection of ideas from statistics and accounting. Finally, the chapter concludes with some suggestions for how to effectively incorporate Benford's law into the curriculum.

Assessing the omission of records from a data set using Benford’s law

2016 ◽  
Vol 23 (4) ◽  
pp. 798-805 ◽  
Author(s):  
Pedro Carreira ◽  
Carlos Gomes da Silva
Keyword(s):  
Tax Evasion ◽  
Original Data ◽  
Economic Crime ◽  
Benford’S Law ◽  
Data Sets ◽  
Data Set ◽  
Content Type ◽  
Benford's Law ◽  
Crime Detection ◽  
Practical Implications

Purpose The purpose of this paper is to propose a methodology to estimate the number of records that were omitted from a data set, and to assess its effectiveness. Design/methodology/approach The procedure to estimate the number of records that were omitted from a data set is based on Benford’s law. Empirical experiments are performed to illustrate the application of the procedure. In detail, two simulated Benford-conforming data sets are distorted and the procedure is then used to recover the original patterns of the data sets. Findings The effectiveness of the procedure seems to increase with the degree of conformity of the original data set with Benford’s law. Practical implications This work can be useful in auditing and economic crime detection, namely in identifying tax evasion. Originality/value This work is the first to propose Benford’s law as a tool to detect data evasion.

Measuring the Quality of European Statistics

Benford's Law ◽  
2015 ◽  
Author(s):  
Bernhard Rauch ◽  
Max Göttsche ◽  
Gernot Brähler ◽  
Stefan Engel
Keyword(s):  
Financial Data ◽  
Benford’S Law ◽  
Data Set ◽  
The Social ◽  
Benford's Law ◽  
Social Statistics ◽  
Government Deficit ◽  
Deficit Spending ◽  
European Statistics

This chapter analyzes Greek statistics which are not relevant to government deficit spending and compare the findings with the results of prior research, which had shown a significant deviation from Benford's law of the first digits distribution of Greek financial statistics. The hypothesis here is that the social data set should conform better with Benford's law than the financial data set, as the incentive for manipulation is lower. However, the results in this chapter show that, in contrast to their financial data, the Greek social statistics data have a good fit with Benford's law. The chapter interprets this outcome as a sign for the effectiveness of the Benford test.

PENERAPAN BENFORD'S LAW UNTUK MENDETEKSI DUGAAN KETIDAKPATUHAN MATERIAL PADA SPT TAHUNAN PPH ORANG PRIBADI

Scientax ◽  
2021 ◽  
Vol 2 (2) ◽  
pp. 140-159
Author(s):  
Adetya Candra Yuwana Putra ◽  
Maryadi
Keyword(s):  
Income Tax ◽  
Quantitative Research ◽  
Benford’S Law ◽  
Data Set ◽  
Individual Income ◽  
Benford's Law ◽  
Inspection Process ◽  
Individual Income Tax ◽  
The Individual ◽  
Return Data

This study aims to examine whether the Individual Income Tax Return data set conforms to the Benford's Law pattern and to examine whether there are indications of material noncompliance in that data set based on the application of Benford's Law. This research is a quantitative research. The data source in this study is the taxation database owned by the Directorate General of Taxes (DGT), Ministry of Finance. The results of this study indicate that most of the Individual Income Tax Return data set variables conform to Benford's Law pattern and there are indications of material noncompliance in that data set. Tax officer, in this case account representatives and tax auditors are expected to be able to use the results of this study to carry out further analysis of the numerical class in the Individual Income Tax Return data set that is not appropriate and deviates from Benford's Law pattern. DGT, as a tax institution, is expected to consider the use of Benford's Law to assist the taxpayer supervision and inspection process.

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