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Hill1996

T. Hill, "A statistical derivation of the significant-digit law," Statistical Science, 10:4 (1996) 354--363.  MR 98a:60021 [Hill demonstrates that if distributions are selected at random, and in turn random samples are taken from these distributions, the significant digits of the combined samples converge to the Benford distribution. He points out this imples the distributions of successive digits also conform to a logarithm law, and so successive digits are not independent. (Note: Statistical Science printed the date incorrectly as 1995, on the whole issue--including the cover!)]