Playing with Benford's Law
Playing with Benford's Law

Summary/Abstract: Benford's Law (BL) can be defined as a collection of empirical evidence related to the frequency distribution of the leading digits in numerical data sets. The best-known version of the law states that in those data sets representing a collection of "natural" data, the probability of seeing a particular digit in the first position is inversely related to its rank. For example, 1 appears as the first digit in about 30% of all cases, while 9 appears in less than 5% of cases. Other versions of BL define the frequency distribution of the second digits, third digits, and their combinations. The history of the discovery of this law makes it even more mysterious. Initially explored by Newcomb (Newcomb & Nuw, 1881), the law was forgotten for more than 50 years. Benford (1938) rediscovered it, and used it to explain the behavior of numerous data sets from different domains of science. BL can be treated as one of the most exciting representations of the power laws, which are used in natural sciences and empirical research in economics (Gabaix, 2016).

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