Benford's Law from Ratios of Random Numbers

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.