Benford law from logarithmic uniformity
= Benford law from logarithmic uniformity
{c}
{title2=$\mathbb P(D=i)=\log_{10}(1+1/i)$}
The leading decimal digit is determined by the fractional part of $\log_{10}X$. A uniform fractional logarithm gives <Benford law> by the lengths of the intervals $[\log_{10}i,\log_{10}(i+1))$. A <log-uniform distribution> whose logarithmic span is an integer has this property. Arbitrary partial-decade truncations generally do not.