# ks.benftest: Kolmogorov-Smirnov Test for Benford's Law In BenfordTests: Statistical Tests for Evaluating Conformity to Benford's Law

## Description

ks.benftest takes any numerical vector reduces the sample to the specified number of significant digits and performs the Kolmogorov-Smirnov goodness-of-fit test to assert if the data conforms to Benford's law.

## Usage

 1 ks.benftest(x = NULL, digits = 1, pvalmethod = "simulate", pvalsims = 10000) 

## Arguments

 x A numeric vector. digits An integer determining the number of first digits to use for testing, i.e. 1 for only the first, 2 for the first two etc. pvalmethod Method used for calculating the p-value. Currently only "simulate" is available. pvalsims An integer specifying the number of replicates used if pvalmethod = "simulate".

## Details

A Kolmogorov-Smirnov test is performed between signifd(x,digits) and pbenf(digits). Specifically:

D = \sup\limits_{i=10^{k-1},…,10^k-1} ≤ft| \displaystyle∑_{j=1}^{i} ( f_j^o - f_j^e ) \right|\cdot √{n}

where f_i^o denotes the observed frequency of digits i, and f_i^e denotes the expected frequency of digits i. x is a numeric vector of arbitrary length. Values of x should be continuous, as dictated by theory, but may also be integers. digits should be chosen so that signifd(x,digits) is not influenced by previous rounding.

## Value

A list with class "htest" containing the following components:

 statistic  the value of the Kolmogorov-Smirnov D test statistic p.value  the p-value for the test method  a character string indicating the type of test performed data.name  a character string giving the name of the data

## References

Benford, F. (1938) The Law of Anomalous Numbers. Proceedings of the American Philosophical Society. 78, 551–572.

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]

Kolmogorov, A.N. (1933) Sulla determinazione empirica di una legge di distibuzione. Giornale dell'Istituto Italiano degli Attuari. 4, 83–91.

pbenf, simulateH0

## Examples

 1 2 3 4 5 6 7 8 #Set the random seed to an arbitrary number set.seed(421) #Create a sample satisfying Benford's law X<-rbenf(n=20) #Perform a Kolmogorov-Smirnov Test on the #sample's first digits using defaults ks.benftest(X) #0.7483 

### Example output

	K-S Test for Benford Distribution

data:  X
D = 0.45182, p-value = 0.7483


BenfordTests documentation built on May 1, 2019, 8:07 p.m.