# zbMATH — the first resource for mathematics

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:
 6e+11 Characteristic functions; other transforms
Full Text: