# CSM-349 - Benford's Law: An Empirical Investigation and a Novel Explanation

@inproceedings{Scott2001CSM349B, title={CSM-349 - Benford's Law: An Empirical Investigation and a Novel Explanation}, author={Pd Scott and Maria Fasli}, year={2001} }

This report describes an investigation into Benford?s Law for the distribution of leading digits in real data sets. A large number of such data sets have been examined and it was found that only a small fraction of them conform to the law. Three classes of mathematical model of processes that might account for such a leading digit distribution have also been investigated. We found that based on the notion of taking the product of many random factors the most credible. This led to the…

## 52 Citations

### An Empirical Non-Parametric Likelihood Family of Data-Based Benford-Like Distributions

- Mathematics
- 2006

A mathematical expression known as Benford's law provides an example of an unexpected relationship among randomly selected sequences of first significant digits (FSDs). Newcomb [Note on the frequency…

### Reality Checks for a Distributional Assumption: The Case of “Benford’s Law”

- Business
- 2013

In recent years, many articles have promoted uses for “Benford’s Law,” claimed to identify a nearly ubiquitous distribution pattern for the frequencies of first digits of numbers in many data sets.…

### An Alternative to the Oversimplifying Benford’s Law in Experimental Fields

- Computer ScienceSankhya B
- 2022

A way to model the distribution of first digits in some naturally occurring collections of data is here highlighted and it is shown that knowing beforehand the values of these bounds enables to find a better adjusted law than Benford's Law.

### Generalized Benford’s Law as a Lie Detector

- MathematicsAdvances in cognitive psychology
- 2017

In two studies, some empirical support for the generalized Benford analysis is provided and it is concluded that familiarity with the numerical domain involved as well as cognitive effort only have a mild effect on the method’s accuracy.

### Benford's Law, Families of Distributions and a Test Basis

- Mathematics
- 2014

Benford's Law is used to test for data irregularities. While novel, there are two weaknesses in the current methodology. First, test values used in practice are too conservative and the test values…

### Remarks on the Use of Benford's Law

- Computer Science
- 2009

An alternative to the usual statistical methodology of digitally analyzing data for conformance with Benford's law is presented, based on the more basic phenomenon underlying the frequency of the first digit, and thus is more robust and powerful.

### Benford's Law as an Instrument for Fraud Detection in Surveys Using the Data of the Socio-Economic Panel (SOEP)

- Economics
- 2010

This paper focuses on fraud detection in surveys using Socio-Economic Panel (SOEP) data as an example for testing newly methods proposed here, and develops a measure that reflects the plausibility of the digit distribution in interviewer clusters and shows that in several SOEP subsamples, Benford's Law holds for the available continuous data.

### Benford’s Law as an Instrument for Fraud Detection in Surveys Using the Data of the Socio-Economic Panel (SOEP)

- Sociology
- 2011

Summary This paper focuses on fraud detection in surveys using Socio-Economic Panel (SOEP) data as an example for testing newly methods proposed here. A statistical theorem referred to as Benford’s…

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

- Computer Science
- 2009

It is suggested that Benford's law does not depend on properties linked with the log function, and two theorems are proved, making up a formal version of this intuition: scattered and regular r.v.'s do approximately follow Benford't law.

### The value of the last digit: statistical fraud detection with digit analysis

- Computer ScienceAdv. Data Anal. Classif.
- 2009

It is proved that last digits are approximately uniform for distributions with an absolutely continuous distribution function, and a result for ‘certain’ sums of lattice-variables as well.

## References

SHOWING 1-10 OF 21 REFERENCES

### A Statistical Derivation of the Significant-Digit Law

- Computer Science
- 1995

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.

### Benford's Law

- Physics, Computer Science
- 2001

It is shown that a number of different statistics associated with computation like space and runtime often follow Benford's Law, and that search cost on input data that follows Benford’s Law is often very different to that on more uniform data.

### On the Distribution of First Significant Digits

- Mathematics
- 1961

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 Application of Fourier Series to the Most Significant Digit Problem

- Mathematics
- 1994

It is an old observation [N] that in tables of logarithms, the first few pages are more smudged and worn than the later pages. It follows that the distribution of the first significant digit of the…

### Base-Invariance Implies Benford's Law

- Mathematics
- 1995

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…

### Evaluating data mining procedures: techniques for generating artificial data sets

- Computer ScienceInf. Softw. Technol.
- 1999

### Statistical distributions

- MathematicsAPLQ
- 1983

The probability integrals are evaluated by series or continued fractions, identified by their equation numbers in Abramowitz and Stegun, and the inverses are obtained by Newtonian iteration.

### On the distribution of numbers

- MathematicsBell Syst. Tech. J.
- 1970

It is shown how the arithmetic operations of a computer transform various distributions toward the limiting distribution of the mantissas of floating point numbers, and a number of applications to hardware, software, and general computing show that this distribution is not merely an amusing curiosity.