scholarly journals Empirical Analysis of Claims Development Trapezoids following Benford’s Law

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Jochen Heberle ◽  
Tobias Gummersbach
Keyword(s):  
Hypothesis Testing ◽  
Empirical Analysis ◽  
Individual Development ◽  
Benford’S Law ◽  
Characteristic Factor ◽  
Wide Range ◽  
Benford's Law ◽  
The Individual

In this paper we make an empirical analysis of a wide range of claims developmenttrapezoids following Benford’s law. In particular we determine Benfors’s law fordifferent characteristic factors depending on claims development triangles/trapezoids.These characteristic factors are the cumulative claims payments, the incrementalclaims payments and the individual development factors. For each characteristic factor hypothesis testing is done for verifying/rejecting 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.

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.

Evaluation of Large-scale Data to Detect Irregularity in Payment for Medical Services

2016 ◽  
Vol 55 (03) ◽  
pp. 284-291
Author(s):  
Junghyun Park ◽  
Seokjoon Yoon ◽  
Minki Kim
Keyword(s):  
Large Scale ◽  
Healthcare Sector ◽  
Benford’S Law ◽  
Individual Level ◽  
Large Scale Data ◽  
Level Data ◽  
Depth Analysis ◽  
Benford's Law ◽  
The Individual ◽  
Scale Data

SummaryBackground: Sophisticated anti-fraud systems for the healthcare sector have been built based on several statistical methods. Although existing methods have been developed to detect fraud in the healthcare sector, these algorithms consume considerable time and cost, and lack a theoretical basis to handle large-scale data.Objectives: Based on mathematical theory, this study proposes a new approach to using Benford’s Law in that we closely examined the individual-level data to identify specific fees for in-depth analysis.Methods: We extended the mathematical theory to demonstrate the manner in which large-scale data conform to Benford’s Law. Then, we empirically tested its applicability using actual large-scale healthcare data from Korea’s Health Insurance Review and Assessment (HIRA) National Patient Sample (NPS). For Benford’s Law, we considered the mean absolute deviation (MAD) formula to test the large-scale data.Results: We conducted our study on 32 diseases, comprising 25 representative diseases and 7 DRG-regulated diseases. We performed an empirical test on 25 diseases, showing the applicability of Benford’s Law to large-scale data in the healthcare industry. For the seven DRG-regulated diseases, we examined the individual-level data to identify specific fees to carry out an in-depth analysis. Among the eight categories of medical costs, we considered the strength of certain irregularities based on the details of each DRG-regulated disease.Conclusions: Using the degree of abnormality, we propose priority action to be taken by government health departments and private insurance institutions to bring unnecessary medical expenses under control. However, when we detect deviations from Benford’s Law, relatively high contamination ratios are required at conventional significance levels.

scholarly journals Benford’s Law in Forensic Analysis of Income Statements of Economic Entities in Bosnia and Herzegovina

2021 ◽  
Vol 23 (1) ◽  
pp. 31-61
Author(s):  
Ševala Isaković-Kaplan ◽  
◽  
Lejla Demirović ◽  
Mahir Proho ◽  
◽  
...  
Keyword(s):  
Bosnia And Herzegovina ◽  
Financial Statements ◽  
Forensic Analysis ◽  
Financial Statement ◽  
Benford’S Law ◽  
Business Decisions ◽  
Full Disclosure ◽  
Wide Range ◽  
Benford's Law ◽  
And Performance

The objective of preparing and presenting financial statements is to provide information about the financial position and performance of an entity, which is useful to a wide range of users of financial statements for business decisions. If information presented in the financial statements is not full disclosure and/or is incorrect, the presented image of the business entity will be wrong, as well as business decisions made on the basis of such financial statements. Unfortunately, many entities knowingly manipulate revenues and expenses to manage earnings in a way that suits the entity management. Detecting frauds in financial statements is the primary task of forensic accountants. This paper analyzes the possibilities of applying Benford’s law in the forensic analysis of income statements of economic entities in Bosnia and Herzegovina, to detect possible earnings manipulation. The results of the research confirm that the positions of revenues and expenses in the income statements of economic entities in Bosnia and Herzegovina generally follow Benford’s law, but also stress the need to increase attention and conduct additional forensic investigations for certain items as indicators of financial statement manipulation.

scholarly journals What Benford Can Tell Us About Cover Pools – An Empirical Analysis

2015 ◽  
Vol 14 (6) ◽  
pp. 829 ◽  
Author(s):  
Stephan Kienle
Keyword(s):  
Empirical Analysis ◽  
Large Data ◽  
Statistical Evidence ◽  
Large Data Sets ◽  
Benford’S Law ◽  
Data Sets ◽  
Benford's Law ◽  
The Empirical Analysis

Leading digits often follow a distribution described by Newcomb (1881) and Benford (1938). We apply this phenomenon known as Benford’s Law on cover assets provided by issuers of German covered bonds. The main finding of the empirical analysis is that leading digits of these assets seem to follow the Benford distribution. Standard statistical evidence, however, might be misleading due to effects of large data sets. Consequently, the present paper also provides an example of how to deal with large data sets when a Benford distribution is assumed. 

When Does the Second-Digit Benford’s Law-Test Signal an Election Fraud?

2011 ◽  
Vol 231 (5-6) ◽  
Author(s):  
Susumu Shikano ◽  
Verena Mack
Keyword(s):  
Statistical Method ◽  
Specific Form ◽  
Benford’S Law ◽  
Parliamentary Election ◽  
Test Results ◽  
Electoral Fraud ◽  
Wide Range ◽  
Benford's Law ◽  
Election Fraud ◽  
Minimal Information

SummaryDetecting election fraud with a simple statistical method and minimal information makes the application of Benford’s Law quite promising for a wide range of researchers. Whilst its specific form, the Second-Digit Benford’s Law (2BL)-test, is increasingly applied to fraud suspected elections, concerns about the validity of its test results have been raised. One important caveat of this kind of research is that the 2BL-test has been applied mostly to fraud suspected elections. Therefore, this article will apply the test to the 2009 German Federal Parliamentary Election against which no serious allegation of fraud has been raised. Surprisingly, the test results indicate that there should be electoral fraud in a number of constituencies. These counter intuitive results might be due to the naive application of the 2BL-test which is based on the conventional χ

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