# simulateH0: Function for Simulating the H0-Distributions needed for... In BenfordTests: Statistical Tests for Evaluating Conformity to Benford's Law

## Description

`simulateH0` is a wrapper function that calculates the specified test statistic under the null hypothesis a certain number of times.

## Usage

 `1` ```simulateH0(teststatistic="chisq", n=10, digits=1, pvalsims=10) ```

## Arguments

 `teststatistic` Which test statistic should be used: "chisq", "edist", "jpsq", "ks", "mdist", "meandigit", or "usq". `n` Sample size of interest. `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. `pvalsims` An integer specifying the number of replicates to be used in simulation.

## Details

Wrapper function that directly outputs the distributions of the specified test statistic under the null hypothesis.

## Value

A vector of length equal to "`pvalsims`".

## 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]

`pbenf`, `chisq.benftest`, `edist.benftest`, `jpsq.benftest`, `ks.benftest`, `mdist.benftest`, \ `meandigit.benftest`, `usq.benftest`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```#Set the random seed to an arbitrary number set.seed(421) #calculate critical value for chisquare test via simulation quantile(simulateH0(teststatistic="chisq", n=100,digits=1,pvalsims=100000),probs=.95) #calculate the "real" critical value qchisq(.95,df=8) #alternatively look at critical values for the jpsq statistic #for different sample sizes (notice the low value for pvalsims) set.seed(421) apply(sapply((1:9)*10,FUN=simulateH0,teststatistic="jpsq", digits=1, pvalsims=100), MARGIN=2,FUN=quantile,probs=.05) ```