Geodesic
Completely asymmetric stable laws and
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 178-184

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Let $Y$ be a random variable with a completely asymmetric stable law and parameter $\alpha$. This paper proves that a probability distribution of a fractional part of the logarithm of $Y$ with respect to any base larger than 1 converges to the uniform distribution on the interval $[0,1]$ for $\alpha\to 0$. This implies that the distribution of the first significant digit of $Y$ for small $\alpha$ can be approximately described by the Benford law.
Keywords: completely asymmetric stable law, Benford law
Mots-clés : Poisson summation formula. 
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     author = {A. A. Kulikova and Yu. V. Prokhorov},
     title = {Completely asymmetric stable laws and},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {178--184},
     publisher = {mathdoc},
     volume = {49},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a11/}
}
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A. A. Kulikova; Yu. V. Prokhorov. Completely asymmetric stable laws and. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 178-184. http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a11/