BenfordTests (version 1.2.0)

BenfordTests-package: Statistical Tests for Benford's Law

Description

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

Details

Package:

BenfordTests

Type:

Package

Version:

1.2.0

Date:

2015-07-18

License:

GPL-3

BenfordTests is the implementation of eight goodness-of-fit (GOF) tests to assess if data conforms to Benford's law.

Tests include: Pearson $\chi^2$ statistic (Pearson, 1900) Kolmogorov-Smirnov D statistic (Kolmogorov, 1933) Freedman's modification of Watson's $U^2$ statistic (Freedman, 1981; Watson, 1961) Chebyshev distance m statistic (Leemis, 2000) Euclidean distance d statistic (Cho and Gaines, 2007) Judge-Schechter mean deviation $a^*$ statistic (Judge and Schechter, 2009) Joenssen's $J_P^2$ statistic, a Shapiro-Francia type correlation test (Shapiro and Francia, 1972) Joint Digit Test $T^2$ statistic, a Hotelling type test (Hotelling, 1931)

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 $\chi^2$, D, $a^*$, and $T^2$ statistics may also be determined using their asymptotic distributions.

References

Benford, F. (1938) The Law of Anomalous Numbers. Proceedings of the American Philosophical Society. 78, 551--572. Cho, W.K.T. and Gaines, B.J. (2007) Breaking the (Benford) Law: Statistical Fraud Detection in Campaign Finance. The American Statistician. 61, 218--223.

Freedman, L.S. (1981) Watson's Un2 Statistic for a Discrete Distribution. Biometrika. 68, 708--711. Joenssen, D.W. (2013) Two Digit Testing for Benford's Law. Proceedings of the ISI World Statistics Congress, 59th Session in Hong Kong. [available under http://www.statistics.gov.hk/wsc/CPS021-P2-S.pdf]

Judge, G. and Schechter, L. (2009) Detecting Problems in Survey Data using Benford's Law. Journal of Human Resources. 44, 1--24. Kolmogorov, A.N. (1933) Sulla determinazione empirica di una legge di distibuzione. Giornale dell'Istituto Italiano degli Attuari. 4, 83--91. Leemis, L.M., Schmeiser, B.W. and Evans, D.L. (2000) Survival Distributions Satisfying Benford's law. The American Statistician. 54, 236--241. Newcomb, S. (1881) Note on the Frequency of Use of the Different Digits in Natural Numbers. American Journal of Mathematics. 4, 39--40. Pearson, K. (1900) 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. 50, 157--175. Shapiro, S.S. and Francia, R.S. (1972) An Approximate Analysis of Variance Test for Normality. Journal of the American Statistical Association. 67, 215--216. Watson, G.S. (1961) Goodness-of-Fit Tests on a Circle. Biometrika. 48, 109--114.

Hotelling, H. (1931). The generalization of Student's ratio. Annals of Mathematical Statistics. 2, 360--378.

Examples

#Set the random seed to an arbitrary number
set.seed(421)
#Create a sample satisfying Benford's law
X<-rbenf(n=20)
#Look at sample
X
#Look at the first digits of the sample
signifd(X)

#Perform a Chi-squared Test on the sample's first digits using defaults
chisq.benftest(X)
#p-value = 0.648