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Balanzario, EP and SŠnchez-Ortiz, J (2010)

Sufficient conditions for Benfordís law

Statistics & Probability Letters 80(23-24), 1713-1719.

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Abstract: We present two sufficient conditions for an absolutely continuous random variable to obey Benfordís law for the distribution of the first significant digit. These two sufficient conditions suggest that Benfordís law will not often be observed in everyday sets of numerical data. On the other hand, we recall that there are two processes by way of which a random variable can come close to following Benfordís law. The first of these is the multiplication of independent random variables and the second is the exponentiation of a random variable to a large power. Our working tool is the Poisson sum formula of Fourier analysis. Like the central limit theorem, Benfordís law has an asymptotic nature.

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Subject Area(s): Probability Theory