• Corpus ID: 18255371

Fundamental Flaws in Feller's Classical Derivation of Benford's Law

  title={Fundamental Flaws in Feller's Classical Derivation of Benford's Law},
  author={Arno Berger and Theodore P. Hill},
  journal={arXiv: Probability},
Feller's classic text 'An Introduction to Probability Theory and its Applications' contains a derivation of the well known significant-digit law called Benford's law. More specifically, Feller gives a sufficient condition ("large spread") for a random variable $X$ to be approximately Benford distributed, that is, for $\log_{10}X$ to be approximately uniformly distributed modulo one. This note shows that the large-spread derivation, which continues to be widely cited and used, contains serious… 

Why the Summation Test Results in a Benford, and not a Uniform Distribution, for Data that Conforms to a Log Normal Distribution

The Summation test consists of adding all numbers that begin with a particular first digit or first two digits and determining its distribution with respect to these first or first two digits

Benford's Law of First Digits: From mathematical Curiosity to Change Detector

It is shown that the distribution of first digits of real world observations would not be uniform, but instead follow a trend where measurements with lower first digit occur more frequently than those with higher first digits.

The Weibull distribution and Benford's law

Benford’s law states that many data sets have a bias towards lower leading digits, with a first digit of 1 about 30.1% of the time and a 9 only 4.6%. There are numerous applications, ranging from

A Widespread Error in the Use of Benford's Law to Detect Election and Other Fraud

The goal of this note is to show that a widespread claim about Benford's Law, namely, that the range of every Benford distribution spans at least several orders of magnitude, is false. The proof is

Benford's law: A “sleeping beauty” sleeping in the dirty pages of logarithmic tables

It is shown that the waking prince is more often quoted than the SB whom he kissed—in this Benford's law case, wondering whether this is a general effect—to be usefully studied.

On the Ability of the Benford’s Law to Detect Earthquakes and Discriminate Seismic Signals

Online Material: Tables of hypocentral parameters; figure showing examples of teleseismic detections using the BLe. Benford’s law (BL), also known as the first‐digit law, is an intriguing pattern in

Out-phased decadal precipitation regime shift in China and the United States

In order to understand the changes in precipitation variability associated with the climate shift around mid-1970s, the precipitation regime changes have been analyzed over both China and the USA.

A conjecture of Sakellaridis–Venkatesh on the unitary spectrum of spherical varieties

We describe the spectral decomposition of certain spherical varieties of low rank, verifying a recent conjecture of Sakellaridis and Venkatesh in these cases.



A Statistical Derivation of the Significant-Digit Law

If distributions are selected at random (in any "unbi- ased" way) and random samples are then taken from each of these dis- tributions, the significant digits of the combined sample will converge to the logarithmic (Benford) distribution.

Large spread does not imply Benford ’ s

Sharp universal bounds are given for the distance between normalised Lebesgue measure on R/Z and the distribution of logX mod 1, where X is uniform. The results dispel the popular belief that a

Base-Invariance Implies Benford's Law

A derivation of Benford's Law or the First-Digit Phenomenon is given assuming only base-invariance of the underlying law. The only baseinvariant distributions are shown to be convex combinations of

A Simple Explanation of Benford's Law

Benfords Law occurs is, however, elusive. Many researchers have verified for themselves that the law is widely obeyed, but have also noted that the popular explanations are not completely satisfying.

On the Distribution of First Significant Digits

Introduction. It has been noticed by astute observers that well used tables of logarithms are invariably dirtier at the front than at the back. Upon reflection one is led to inquire whether there are

An Introduction to Probability Theory and Its Applications

Thank you for reading an introduction to probability theory and its applications vol 2. As you may know, people have look numerous times for their favorite novels like this an introduction to

An introduction to probability theory

This classic text and reference introduces probability theory for both advanced undergraduate students of statistics and scientists in related fields, drawing on real applications in the physical and


La loi dite « de Benford » s’applique a une variable X dont le logarithme a une partie fractionnaire uniforme. Il a ete montre qu’elle s’applique approximativement a de nombreuses series numeriques

The Art of Computer Programming

The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.

When Can One Test an Explanation? Compare and Contras Benford’s Law and the Fuzzy CLT

Testing a proposed explanation of a statistical phenomenon is conceptually difficult. This class segment is intended to spotlight the issues. This article has supplementary material online.