scholarly journals Benford’s law first significant digit and distribution distances for testing the reliability of financial reports in developing countries

2018 ◽  
Vol 492 ◽  
pp. 878-888 ◽  
Author(s):  
Jing Shi ◽  
Marcel Ausloos ◽  
Tingting Zhu
Keyword(s):  
Developing Countries ◽  
Benford’S Law ◽  
Financial Reports ◽  
Significant Digit ◽  
Benford's Law

Abiding by the Law? Using Benford’s Law to Examine the Accuracy of Nonprofit Financial Reports

2019 ◽  
Vol 49 (3) ◽  
pp. 548-570 ◽  
Author(s):  
Heng Qu ◽  
Richard Steinberg ◽  
Ronelle Burger
Keyword(s):  
Statistical Methods ◽  
Organizational Level ◽  
Benford’S Law ◽  
Financial Reports ◽  
Forensic Accounting ◽  
Data Form ◽  
Benford's Law ◽  
Natural Data ◽  
The Individual ◽  
Academic Study

Benford’s Law asserts that the leading digit 1 appears more frequently than 9 in natural data. It has been widely used in forensic accounting and auditing to detect potential fraud, but its application to nonprofit data is limited. As the first academic study that applies Benford’s Law to U.S. nonprofit data (Form 990), we assess its usefulness in prioritizing suspicious filings for further investigation. We find close conformity with Benford’s Law for the whole sample, but at the individual organizational level, 34% of the organizations do not conform. Deviations from Benford’s law are smaller for organizations that are more professional, that report positive fundraising and administration expenses, and that face stronger funder oversight. We suggest improved statistical methods and experiment with a new measure of the extent of deviation from Benford’s Law that has promise as a more discriminating screening metric.

scholarly journals Comment on “Benford's Law and the Detection of Election Fraud”

2011 ◽  
Vol 19 (3) ◽  
pp. 269-272 ◽  
Author(s):  
Walter R. Mebane
Keyword(s):  
Careful Analysis ◽  
Benford’S Law ◽  
Simulation Exercise ◽  
Strategic Actions ◽  
Significant Digit ◽  
Benford's Law ◽  
The Mean ◽  
Election Fraud ◽  
Open Question

“Benford's Law and the Detection of Election Fraud” raises doubts about whether a test based on the mean of the second significant digit of vote counts equals 4.187 is useful as a test for the occurrence of election fraud. The paper mistakenly associates such a test with Benford's Law, considers a simulation exercise that has no apparent relevance for any actual election, applies the test to inappropriate levels of aggregation, and ignores existing analysis of recent elections in Russia. If tests based on the second significant digit of precinct-level vote counts are diagnostic of election fraud, the tests need to use expectations that take into account the features of ordinary elections, such as strategic actions. Whether the tests are useful for detecting fraud remains an open question, but approaching this question requires an approach more nuanced and tied to careful analysis of real election data than one sees in the discussed paper.

An Introduction to Benford's Law

2015 ◽  
Author(s):  
Arno Berger ◽  
Theodore P. Hill
Keyword(s):  
Random Variables ◽  
Benford’S Law ◽  
Late Nineteenth Century ◽  
Comprehensive Treatment ◽  
Open Problems ◽  
Significant Digit ◽  
Wide Range ◽  
Benford's Law ◽  
Primary Reference ◽  
Basic Facts

This book provides the first comprehensive treatment of Benford's law, the surprising logarithmic distribution of significant digits discovered in the late nineteenth century. Establishing the mathematical and statistical principles that underpin this intriguing phenomenon, the text combines up-to-date theoretical results with overviews of the law's colorful history, rapidly growing body of empirical evidence, and wide range of applications. The book begins with basic facts about significant digits, Benford functions, sequences, and random variables, including tools from the theory of uniform distribution. After introducing the scale-, base-, and sum-invariance characterizations of the law, the book develops the significant-digit properties of both deterministic and stochastic processes, such as iterations of functions, powers of matrices, differential equations, and products, powers, and mixtures of random variables. Two concluding chapters survey the finitely additive theory and the flourishing applications of Benford's law. Carefully selected diagrams, tables, and close to 150 examples illuminate the main concepts throughout. The book includes many open problems, in addition to dozens of new basic theorems and all the main references. A distinguishing feature is the emphasis on the surprising ubiquity and robustness of the significant-digit law. The book can serve as both a primary reference and a basis for seminars and courses.

scholarly journals The empirical analysis of financial reports of companies in Croatia: Benford distribution curve as a benchmark for first digits

2019 ◽  
Vol 5 (2) ◽  
pp. 90-100
Author(s):  
Ivana Cunjak Mataković
Keyword(s):  
Distribution Curve ◽  
Stock Exchange ◽  
Financial Statements ◽  
Benford’S Law ◽  
Chi Square ◽  
Financial Reports ◽  
Benford's Law ◽  
Chi Square Test ◽  
Kolmogorov Smirnov ◽  
The Empirical Analysis

AbstractThe financial numbers game is unfortunately alive and doing well. One of the forensic accounting techniques is based on Benford’s Law and is used for the detection of unusual transactions, anomalies or trends. The aim of this paper is to test whether the financial statements of Croatian companies deviate from Benford’s Law distribution. The financial statements of 24 companies that are in the pre-bankruptcy settlement process and 24 companies that are not in the pre-bankruptcy settlement process were analysed using the Benford’s Law test of the first digit distribution for the period from 2015 to 2018. The data used to calculate the first digits of distribution were taken from the Zagreb Stock Exchange. The chi-square test has shown that the observed companies that are not in the process of pre-bankruptcy settlement do not have the first digit distribution which follows the Benford’s Law distribution. The Kolmogorov-Smirnov Z test has shown that the distribution of the first digits from the financial statements of companies listed on the Zagreb Stock Exchange fits to Benford’s Law distribution.

EARNINGS MANAGEMENT AMONG FIRMS DURING THE PRE-SEC ERA: A BENFORD'S LAW ANALYSIS

2011 ◽  
Vol 38 (2) ◽  
pp. 145-170 ◽  
Author(s):  
Jeffrey J. Archambault ◽  
Marie E. Archambault
Keyword(s):  
Financial Statement ◽  
Benford’S Law ◽  
Operating Environment ◽  
Industrial Firms ◽  
Financial Reports ◽  
Rate Regulation ◽  
Time Period ◽  
Benford's Law ◽  
Utility Companies ◽  
Net Assets

ABSTRACT This paper examines the existence of financial statement manipulation in the U.S. during a time period when many of the current motivations did not exist. The study looks for types of manipulations that would be motivated by the pre-SEC operating environment. To examine this issue, a sample of U.S. firms from the 1915 Moody's Analyses of Investments is divided into industrial firms, railroads, and utilities. The railroad and utility companies faced rate regulation during this time period, providing incentives to manipulate the financial reports so as to maximize the rate received. Industrial firms were not regulated. These companies wanted to attract investors, motivating manipulations to increase income and net assets. To determine if manipulations are occurring, a Benford's Law analysis is used. This analysis examines the frequency of numbers in certain positions within an amount to determine if the distribution of the numbers is similar to the pattern documented by Benford's Law. Some manipulations consistent with expectations are found.

Random-Number Guessing and the First Digit Phenomenon

1988 ◽  
Vol 62 (3) ◽  
pp. 967-971 ◽  
Author(s):  
Theodore P. Hill
Keyword(s):  
Random Number ◽  
Benford’S Law ◽  
Empirical Observation ◽  
Significant Digit ◽  
Physical Constants ◽  
Benford's Law ◽  
Empirical Regularities ◽  
Newspaper Articles

To what extent do individuals “absorb” the empirical regularities of their environment and reflect them in behavior? A widely-accepted empirical observation called the First Digit Phenomenon or Benford's Law says that in collections of miscellaneous tables of data (such as physical constants, almanacs, newspaper articles, etc.), the first significant digit is much more likely to be a low number than a high number. In this study, an analysis of the frequencies of the first and second digits of “random” six-digit numbers guessed by people suggests that people's responses share some of the properties of Benford's Law: first digit 1 occurs much more frequently than expected; first digit 8 or 9 occurs much less frequently; and the second digits are much more uniformly distributed than the first.

scholarly journals Fraud Detection in Financial Statements Applying Benford's Law with Monte Carlo Simulation

2019 ◽  
Vol 69 (2) ◽  
pp. 217-239
Author(s):  
Vladan Pavlović ◽  
Goranka Knežević ◽  
Marijana Joksimović ◽  
Dušan Joksimović
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Frequency Distribution ◽  
High Probability ◽  
Financial Statements ◽  
Financial Statement ◽  
Benford’S Law ◽  
Financial Reports ◽  
Benford's Law ◽  
Very High

Benford's Law is a useful tool for detecting fraud in financial statements. In this paper we test the financial item named ‘Work performed by the undertaking for its own purpose and capitalised’ applying this tool. The data are taken from the financial reports of all companies submitted to the Serbian Business Register Agency for the period of 2008–2013. Our conclusion shows that there is a very high probability that the frequency distribution of the second digit does not satisfy Benford's Law. In other words, it implies that certain manipulations have been usually done with the second digit of the aforementioned item in the financial statement. This research confirms our hypothesis that financial statement frauds are usually conducted using the second digit.

scholarly journals Benford’s law in the Gaia universe

2020 ◽  
Vol 642 ◽  
pp. A205
Author(s):  
Jurjen de Jong ◽  
Jos de Bruijne ◽  
Joris De Ridder
Keyword(s):  
Bayesian Approach ◽  
Dynamic Range ◽  
Zero Point ◽  
Atomic Data ◽  
Benford’S Law ◽  
Selection Function ◽  
Significant Digit ◽  
Benford's Law ◽  
The Difference ◽  
Digit Frequencies

Context. Benford’s law states that for scale- and base-invariant data sets covering a wide dynamic range, the distribution of the first significant digit is biased towards low values. This has been shown to be true for wildly different datasets, including financial, geographical, and atomic data. In astronomy, earlier work showed that Benford’s law also holds for distances estimated as the inverse of parallaxes from the ESA HIPPARCOS mission. Aims. We investigate whether Benford’s law still holds for the 1.3 billion parallaxes contained in the second data release of Gaia (Gaia DR2). In contrast to previous work, we also include negative parallaxes. We examine whether distance estimates computed using a Bayesian approach instead of parallax inversion still follow Benford’s law. Lastly, we investigate the use of Benford’s law as a validation tool for the zero-point of the Gaia parallaxes. Methods. We computed histograms of the observed most significant digit of the parallaxes and distances, and compared them with the predicted values from Benford’s law, as well as with theoretically expected histograms. The latter were derived from a simulated Gaia catalogue based on the Besançon galaxy model. Results. The observed parallaxes in Gaia DR2 indeed follow Benford’s law. Distances computed with the Bayesian approach of Bailer-Jones et al. (2018, AJ, 156, 58) no longer follow Benford’s law, although low-value ciphers are still favoured for the most significant digit. The prior that is used has a significant effect on the digit distribution. Using the simulated Gaia universe model snapshot, we demonstrate that the true distances underlying the Gaia catalogue are not expected to follow Benford’s law, essentially because the interplay between the luminosity function of the Milky Way and the mission selection function results in a bi-modal distance distribution, corresponding to nearby dwarfs in the Galactic disc and distant giants in the Galactic bulge. In conclusion, Gaia DR2 parallaxes only follow Benford’s Law as a result of observational errors. Finally, we show that a zero-point offset of the parallaxes derived by optimising the fit between the observed most-significant digit frequencies and Benford’s law leads to a value that is inconsistent with the value that is derived from quasars. The underlying reason is that such a fit primarily corrects for the difference in the number of positive and negative parallaxes, and can thus not be used to obtain a reliable zero-point.

Benford's Law

2015 ◽  
Keyword(s):  
Stock Prices ◽  
Mortality Rates ◽  
Benford’S Law ◽  
Data Sets ◽  
Financial Reports ◽  
Medical Tests ◽  
Benford's Law ◽  
Technical Details ◽  
The Many ◽  
Population Numbers

Benford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from electricity bills and street addresses to stock prices, population numbers, mortality rates, and the lengths of rivers. This book demonstrates the many useful techniques that arise from the law, showing how truly multidisciplinary it is, and encouraging collaboration. Beginning with the general theory, the chapters explain the prevalence of the bias, highlighting explanations for when systems should and should not follow Benford's law and how quickly such behavior sets in. The book goes on to discuss important applications in disciplines ranging from accounting and economics to psychology and the natural sciences. The book describes how Benford's law has been successfully used to expose fraud in elections, medical tests, tax filings, and financial reports. Additionally, numerous problems, background materials, and technical details are available online to help instructors create courses around the book. Emphasizing common challenges and techniques across the disciplines, this book shows how Benford's law can serve as a productive meeting ground for researchers and practitioners in diverse fields.

Sign in / Sign up

Export Citation Format

Share Document