The value of the last digit: statistical fraud detection with digit analysis

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 (1997) made use of Benford’s Law (Benford 1938) as a natural reference distribution. A justification of that hypothesis is only known for multiplicative sequences (Schatte 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 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.