A Laplace-transform derivation shows that "well-behaved" probability distributions approximately satisfy Benford's law, P(d) = log10(1 + 1/d).
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A Proof of First Digit Law from Laplace Transform
A Laplace-transform derivation shows that "well-behaved" probability distributions approximately satisfy Benford's law, P(d) = log10(1 + 1/d).