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An invariant-sum characterization of Benford’s law. (English) Zbl 0874.60016
Summary: The accountant Nigrini remarked that in tables of data distributed according to Benford’s law, the sum of all elements with first digit \(d\) \((d=1,2,\dots,9)\) is approximately constant. A mathematical formulation of Nigrini’s observation is given and it is shown that Benford’s law is the unique probability distribution such that the expected sum of all elements with first digits \(d_1,\dots,d_k\) is constant for every fixed \(k\).

MSC:
60E10 Characteristic functions; other transforms
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