The Value of the Last Digit. Statistical Fraud Detection with Digit Analysis

Dlugosz S, Müller-Funk U


Abstract
Digit distributions are a popular tool for the detection of tax payers' noncompliance and other fraud. In the early stage of digital analysis, Nigrini and Mittermaier (A J Pract Theory 16(2):52-67, 1997) made use of Benford's Law (Benford in Am Philos Soc 78:551-572, 1938) as a natural reference distribution. A justification of that hypothesis is only known for multiplicative sequences (Schatte in J Inf Process Cyber EIK 24:443-455, 1988). In applications, most of the number generating processes are of an additive nature and no single choice of ‘an universal first-digit law' seems to be plausible (Scott and Fasli in Benford's law: an empirical investigation and a novel explanation. CSM Technical Report 349, Department of Computer Science, University of Essex,http://cswww.essex.ac.uk/technical-reports/2001/CSM-349.pdf, 2001). In that situation, some practioneers (e.g. financial authorities) take recourse to a last digit analysis based on the hypothesis of a Laplace distribution. We prove that last digits are approximately uniform for distributions with an absolutely continuous distribution function. From a practical perspective, that result, of course, is only moderately interesting. For that reason, we derive a result for ‘certain' sums of lattice-variables as well. That justification is provided in terms of stationary distributions.

Keywords
Fraud detection, Last digits, Digit analysis, Benford’s law



Publication type
Article in Journal

Peer reviewed
Yes

Publication status
Published

Year
2009

Journal
Advances in Data Analysis and Classification

Volume
3

Issue
3

Book title
Advances in Data Analysis and Classification

Editor
Bock H H, Gaul W, Okada A, Vichi M

Start page
281

End page
290

Publisher
Springer

Place
Berlin, Heidelberg

Language
English

ISSN
1862-5347

DOI