Sufficient conditions for Benford's law

被引：5

作者：

Balanzario, Eugenio P. ^{[1
]}

Sanchez-Ortiz, Jorge ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Unidad Morelia, Inst Matemat, Morelia 58089, Michoacan, Mexico

来源：

STATISTICS & PROBABILITY LETTERS | 2010年 / 80卷 / 23-24期

关键词：

Benford's law; First significant digit;

D O I：

10.1016/j.spl.2010.07.014

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We present two sufficient conditions for an absolutely continuous random variable to obey Benford's law for the distribution of the first significant digit. These two sufficient conditions suggest that Benford's 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 Benford's 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. Benford's law has an asymptotic nature. (c) 2010 Elsevier B.V. All rights reserved.

引用

页码：1713 / 1719

页数：7