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On the significands of uniform random variables

  • Arno Berger (a1) and Isaac Twelves (a1)


For all α > 0 and real random variables X, we establish sharp bounds for the smallest and the largest deviation of αX from the logarithmic distribution also known as Benford's law. In the case of uniform X, the value of the smallest possible deviation is determined explicitly. Our elementary calculation puts into perspective the recurring claims that a random variable conforms to Benford's law, at least approximately, whenever it has large spread.


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* Postal address: Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
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On the significands of uniform random variables

  • Arno Berger (a1) and Isaac Twelves (a1)


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