Benford's Law
Loading...
Authors
Silverman, Aaron
Issue Date
2008
Type
Thesis
Language
en_US
Keywords
Alternative Title
Abstract
Some time around 1881, Simon Newcomb (1) was flipping through logarithmic tables and was struck at how much more quickly the first tables wear out than the subsequent ones. After some investigation, he found that the reason lay in the frequency of digits in the natural numbers. To quote “the fist significant figure is oftener 1 than any other digit, and the frequency diminishes up to nine. 1”
By noticing that the frequency of lookups in anti-logarithm tables was completely uniform, Newcomb was able to infer the following law: that the first significant digits in a random tabulation of data obey a logarithmic distribution, with 1 being the most common, at 30.1% and frequency decreasing for digits up to 9 with frequency 4.5%.
He gave a table of frequencies, but no algebraic formulation of the law and practically no theoretical justification. The paper was duly forgotten, and no more significant developments came to light for 57 more years, until in 1938 a researcher named Frank Benford (2) at the General Electric Company laboratories in Schenectady, New York collected 20 different collected data sets such as the area of rivers, constants, or addresses of the first 342 names mentioned in American Men of Science. Averaging all these numbers out, he observed the same curve as Newcomb.
Description
31 leaves
Citation
Publisher
License
U.S. copyright laws protect this material. Commercial use or distribution of this material is not permitted without prior written permission of the copyright holder.