Scatter and regularity imply Benford's law... and more

Details Scatter and regularity imply Benford's law... and more Scatter and regularity imply Benford's law... and more

2009-10-07

arxiv.org/abs/0910.1359v1

Mathematics

Probability

Scientific paper

A random variable (r.v.) X is said to follow Benford's law if log(X) is uniform mod 1. Many experimental data sets prove to follow an approximate version of it, and so do many mathematical series and continuous random variables. This phenomenon received some interest, and several explanations have been put forward. Most of them focus on specific data, depending on strong assumptions, often linked with the log function. Some authors hinted - implicitly - that the two most important characteristics of a random variable when it comes to Benford are regularity and scatter. In a first part, we prove two theorems, making up a formal version of this intuition: scattered and regular r.v.'s do approximately follow Benford's law. The proofs only need simple mathematical tools, making the analysis easy. Previous explanations thus become corollaries of a more general and simpler one. These results suggest that Benford's law does not depend on properties linked with the log function. We thus propose and test a general version of the Benford's law. The success of these tests may be viewed as an a posteriori validation of the analysis formulated in the first part.

Affiliated with

Also associated with

No associations

Rating

Scatter and regularity imply Benford's law... and more does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Scatter and regularity imply Benford's law... and more, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scatter and regularity imply Benford's law... and more will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-351767