Newcomb–Benford law helps customs officers to detect fraud in international trade

The leading digit of a number represents its nonzero leftmost digit. For example, the leading digits of 19 and 0.072 are 1 and 7, respectively. The Newcomb–Benford law (NBL) was originally discovered in the late 19th century (1, 2) as an anecdotal pattern emerging in such seemingly disparate datasets as streets addresses, freezing points of chemical compounds, house prices, and physical constants, with the leading digit, d , in those datasets following a logarithmically decaying distribution, P ( d ) = log10(1 + 1/ d ), instead of being uniformly distributed, as one may naively assume. Later, this pattern was shown to be a consequence of a central limit-type mechanism (3⇓–5), emerging not only empirically but also in mathematical sequences of several garments. A few years ago, some authors devised a way to leverage the NBL as an antifraud tool (6, 7), based on a simple idea: Assuming that this law is expected to naturally emerge in a certain dataset, the statistics would deviate from the law in a way that could be quantitatively measured when the dataset has been manipulated or when data have been fabricated. Accordingly, the NBL and variants have been proposed to assess fraud in contexts ranging from election data (8⇓⇓–11) to financial accounting in external, internal, and governmental auditing (12). In PNAS, Cerioli et al. (13) take this strategy to the next level, proposing a sophisticated statistical modeling framework that can be used to monitor and detect hints of individual fraudulent behavior in the context of international trade (i.e., imports and exports that are declared by national traders and shipping agents). Cerioli et al. developed a mathematical model that provides the correct statistical tests to assess conformance of individual traders to the NBL and then validated the … [↵][1]1Email: l.lacasa{at}qmul.ac.uk. [1]: #xref-corresp-1-1