Goodness-of-fit testing for the Newcomb-Benford law with application to the detection of customs fraud

The Newcomb-Benford law for digit sequences has recently attracted interest in anti-fraud analysis. However, most of its applications rely either on diagnostic checks of the data, or on informal decision rules. We suggest a new way of testing the Newcomb-Benford law that turns out to be particularly attractive for the detection of frauds in customs data collected from international trade. Our approach has two major advantages. The first one is that we control the rate of false rejections at each stage of the procedure, as required in anti-fraud applications. The second improvement is that our testing procedure leads to exact significance levels and does not rely on large-sample approximations. Another contribution of our work is the derivation of a simple expression for the digit distribution when the Newcomb-Benford law is violated, and a bound for a chi-squared type of distance between the actual digit distribution and the Newcomb-Benford one.