Chapter 5

Benford's Law

The Basics

The Benford's Law–based tests signal abnormal duplications. The mathematics of Benford's Law gives us the expected or the normal duplications, and duplications above the norm are abnormal or excessive. Bolton and Hand (2002) state that the statistical tools for fraud detection all have a common theme in that observed values are usually compared to a set of expected values. They also say that depending on the context, these expected values can be derived in various ways and could vary on a continuum from single numerical or graphical summaries all the way to complex multivariate behavior profiles. They contrast supervised methods of fraud detection that use samples of both fraudulent and nonfraudulent records, or unsupervised methods that identify transactions or customers that are most dissimilar to some norm (i.e., outliers). They are correct when they say that we can seldom be certain by statistical analysis alone that a fraud has been perpetrated. The forensic analysis should give us an alert that a record is anomalous, or more likely to be fraudulent than others, so that it can be investigated in more detail. The authors suggest the concept of a suspicion score where higher scores are correlated with records that are more unusual or more like previous fraudulent values. Suspicion scores could be computed for each record in a table and it would be most cost-effective to concentrate on the records with the highest scores. Their overview of ...

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