Googling Benford’s Law brings up a link to a very elementary, but quite illuminating, paper by R. M. Fewster “A Simple Explanation of Benford’s Law”, who gives a very simple explanation to why it should hold ( the different digits correspond to “stripes” of different width, in the range [n,n+1] for all integer n, on the graph of the p.d.f. of log(X), where X is the random variable in question – if the p.d.f. of log(X) is “smooth enough” – for example log(X) is NOT smooth is this sense when X is distributed uniformly – Benford’s law just comes out from the hat). The big advantage of such an intuitive explanation, in what regards myself, that by just inspecting the distribution of log(X), also for X generated artificially (I played with various distributions plotting their histograms in R), one may already tell with some accuracy whether some approximation to Benford’s law holds for such distribution.
Probably this is already contained in the present blog entry, but Fewster article was for me easier to follow.

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