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.

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.

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.

Benfordʼs Law Geometry

Benford's Law ◽  
2015 ◽  
Author(s):  
Lawrence Leemis
Keyword(s):  
Empirical Data ◽  
Probability Distributions ◽  
Benford’S Law ◽  
Data Sets ◽  
Normal Distributions ◽  
Benford's Law ◽  
Using Data

This chapter switches from the traditional analysis of Benford's law using data sets to a search for probability distributions that obey Benford's law. It begins by briefly discussing the origins of Benford's law through the independent efforts of Simon Newcomb (1835–1909) and Frank Benford, Jr. (1883–1948), both of whom made their discoveries through empirical data. Although Benford's law applies to a wide variety of data sets, none of the popular parametric distributions, such as the exponential and normal distributions, agree exactly with Benford's law. The chapter thus highlights the failures of several of these well-known probability distributions in conforming to Benford's law, considers what types of probability distributions might produce data that obey Benford's law, and looks at some of the geometry associated with these probability distributions.

Benford’s Law and Stock Market—The Implications for Investors: The Evidence from India Nifty Fifty

2018 ◽  
Vol 7 (2) ◽  
pp. 103-121
Author(s):  
M. Jayasree ◽  
C. S. Pavana Jyothi ◽  
P. Ramya
Keyword(s):  
Stock Returns ◽  
Stock Prices ◽  
Moving Average ◽  
Benford’S Law ◽  
Business Research ◽  
Volume Number ◽  
Accounting Numbers ◽  
Benford's Law ◽  
Money Flow ◽  
Exhaustive Study

Benford’s law which is also known as first digit law states that data follow a certain frequency. This law was applied to accounting by Nigrini (2012, Benford’s Law: Applications for forensic accounting, auditing, and fraud detection [Vol. 586], John Wiley & Sons) and later on, an exhaustive study was carried out by Amiram, Bozanic, and Rouen (2015, Review of Accounting Studies, 20(4), 1540–1593) to explore the applicability of the law to detect accounting frauds which was proven to be working. The literature has substantial evidence on relationship between accounting numbers and stock returns. The application of Benford’s law to stock trade and returns was explored and it was found that stock trade that included volume, number of trades, and turnover confirmed the distribution but stock returns did not conform the distribution (Jayasree, 2017, Jindal Journal of Business Research, 6(2), 172–186). In this context, the present study attempts to understand its implications to investors by examining the three-day moving average of stock prices and volatility volume by using Chainkin money flow during announcement and post-announcement period of observation. The study also examines whether stocks conforming the distribution and stocks not conforming the distribution are significantly different in buying and selling.

Detecting Fraud in Data Sets Using Benford's Law

2004 ◽  
Vol 33 (1) ◽  
pp. 229-246 ◽  
Author(s):  
Christina Lynn Geyer ◽  
Patricia Pepple Williamson
Keyword(s):  
Benford’S Law ◽  
Data Sets ◽  
Benford's Law

scholarly journals Inconsistencies in countries COVID-19 data revealed by Benford’s law

2021 ◽  
Vol 16 (1) ◽  
pp. 73-79
Author(s):  
Vitor Hugo Moreau
Keyword(s):  
Large Data ◽  
Large Data Sets ◽  
Benford’S Law ◽  
Data Sets ◽  
Data Corruption ◽  
Health Authorities ◽  
Benford's Law ◽  
Crucial Information

Reporting of daily new cases and deaths on COVID-19 is one of the main tools to understand and menage the pandemic. However, governments and health authorities worldwide present divergent procedures while registering and reporting their data. Most of the bias in those procedures are influenced by economic and political pressures and may lead to intentional or unintentional data corruption, what can mask crucial information. Benford’s law is a statistical phenomenon, extensively used to detect data corruption in large data sets. Here, we used the Benford’s law to screen and detect inconsistencies in data on daily new cases of COVID-19 reported by 80 countries. Data from 26 countries display severe nonconformity to the Benford’s law (p< 0.01), what may suggest data corruption or manipulation.

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.

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.

scholarly journals A data transformation process for using Benford’s Law with bounded data

2021 ◽  
Vol 3 ◽  
pp. 29
Author(s):  
Daniel McCarville
Keyword(s):  
Oral Language ◽  
Transformation Process ◽  
Benford’S Law ◽  
Data Sets ◽  
Empirical Observation ◽  
Assessment Scores ◽  
Education Data ◽  
Benford's Law ◽  
Forensic Scientists ◽  
Bounded Data

Benford’s Law is an empirical observation about the frequency of digits in a variety of naturally occurring data sets. Auditors and forensic scientists have used Benford’s Law to detect erroneous data in accounting and legal usage. One well-known limitation is that Benford’s Law fails when data have clear minimum and maximum values. Many kinds of education data, including assessment scores, typically include hard maximums and therefore do not meet the parametric assumptions of Benford’s Law. This paper implements a transformation procedure which allows for assessment data to be compared to Benford’s Law. As a case study, a data quality assessment of oral language scores from the Early Childhood Longitudinal Study, Kindergarten (ECLS-K) study is used and higher risk data segments detected. The same method could be used to evaluate other concerns, such as test fraud, or other bounded datasets.

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