BenfordTests (version 0.5)

BenfordTests-package: Statistical Tests for Benford's Law.

Description

This package contains seven specialized statistical tests and support functions for determining if numerical data could conform to Benford's law.

Details

ll{ Package: BenfordTests Type: Package Version: 0.5 Date: 2013-04-09 License: GPL-3 } BenfordTests is the implementation of the seven most commonly used goodness-of-fit (GOF) tests to assess if data conforms to Benford's law. Tests include: Pearson chi-square statistic (Pearson (1900)) Kolmogorov-Smirnov D statistic (Kolmogorov (1933)) Freedman's modification of Watson's U-square statistic (Freedman (1981), Watson (1961)) Chebyshev distance m statistic (Leemis (2000)) Euclidean distance d statistic (Cho and Gaines (2007)) Judge-Schechter mean deviation a-star statistic (Judge and Schechter (2009)) Joenssen's JP-square statistic, a Shapiro-Francia type correlation test (Shapiro and Francia (1972)) All tests may be performed using more than one leading digit. All tests simulate the specific p-values required for statistical inference, while p-values for the chi-square and D statistics may also be determined using their asymptotic distributions. The package version numbers are indicative of performance and breadth of functions.

References

Benford F. The law of anomalous numbers. Proceedings of the American Philosophical Society. 1938;78:551-572. Cho WKT, Gaines BJ. Breaking the (Benford) law: Statistical fraud detection in campaign finance. The American Statistician. 2007;61(4):218-223. Freedman LS. Watson's Un2 statistic for a discrete distribution. Biometrika. 1981;68(3):708-711. Judge G, Schechter L. Detecting problems in survey data using Benford's law. Journal of Human Resources. 2009;44:1-24. Kolmogorov AN. Sulla determinazione empirica di una legge di distibuzione. Giornale dell'Istituto Italiano degli Attuari. 1933;4:83-91. Leemis LM, Schmeiser BW, Evans DL. Survival distributions satisfying Benford's law. The American Statistician. 2000;54(4):236-241. Newcomb S. Note on the frequency of use of the different digits in natural numbers. American Journal of Mathematics. 1881;4(1):39-40. Pearson K. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine Series 5. 1900;50(302):157-175. Shapiro SS, Francia RS. An approximate analysis of variance test for normality. Journal of the American Statistical Association. 1972;67:215-216. Watson GS. Goodness-of-fit tests on a circle. Biometrika. 1961;48:109-114.

Examples

#Create a sample satisfying Benford's law
X<-rbenf(n=20)
X
#Look at the first digits of the sample
leading_digits(X)

#Perform a Chi-squared Test on the sample's first digits 
chi_square_benford(X)