BASE-INVARIANCE IMPLIES BENFORDS LAW

被引：134

作者：

HILL, TP

机构：

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1995年 / 123卷 / 03期

关键词：

FIRST-DIGIT PROBLEM; BASE-INVARIANCE; SCALE-INVARIANCE; BENFORDS LAW; INVARIANT MEASURE; NTH DIGIT LAW;

D O I：

10.2307/2160815

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A derivation of Benford's Law or the First-Digit Phenomenon is given assuming only base-invariance of the underlying law. The only base-invariant distributions are shown to be convex combinations of two extremal probabilities, one corresponding to point mass and the other a log-lebesgue measure. The main tools in the proof are identification of an appropriate mantissa sigma-algebra on the positive reals, and results for invariant measures on the circle.

引用

页码：887 / 895

页数：9

共 9 条

[1]

Benford F., 1938, P AM PHIL SOC, V78, P551

[2] EXPLANATION OF 1ST DIGIT PHENOMENON [J].