Benford's Law from Ratios of Random Numbers

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Simon Newcomb believed that the empirical regularity later known as Benford's Law arises because the data exhibiting the law are ratios of random quantities. A computer experiment can be set up to test Newcomb's hypothesis. Ratios are formed using numbers randomly drawn from a random segment of the unit interval. The distribution of the leading digits of the ratios is represented by the blue line. The purple line represents Benford's Law.

Contributed by: Fiona Maclachlan (March 2011)
Open content licensed under CC BY-NC-SA



The ratios are formed using numbers drawn from a random segment of the unit interval. Drawing from a fixed interval results in a distribution of leading digits given by , where s is the value of the leading digit.

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