Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/Benford_tests.R

`jpsq.benftest`

takes any numerical vector reduces the sample to the specified number of significant digits and performs a goodness-of-fit test based on the correlation between the first digits' distribution and Benford's distribution to assert if the data conforms to Benford's law.

1 | ```
jpsq.benftest(x = NULL, digits = 1, pvalmethod = "simulate", pvalsims = 10000)
``` |

`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 |

`pvalsims` |
An integer specifying the number of replicates used if |

A statistical test is performed utilizing the sign-preserved squared correlation between `signifd(x,digits)`

and `pbenf(digits)`

.
Specifically:

*J_P^2=sgn≤ft(cor≤ft(f^o, f^e\right)\right)\cdot cor≤ft(f^o, f^e\right) ^2*

where *f^o* denotes the observed frequencies and *f^e* denotes the expected frequency of digits

*10^{k-1},10^{k-1}+1,…,10^k-1*.
`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.

A list with class "`htest`

" containing the following components:

`statistic ` |
the value of the |

`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 |

Dieter William Joenssen Dieter.Joenssen@googlemail.com

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

Joenssen, D.W. (2013) A New Test for Benford's Distribution. In: *Abstract-Proceedings of the 3rd Joint Statistical Meeting DAGStat, March 18-22, 2013*; Freiburg, Germany.

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]

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.

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 Joenssen's \emph{JP-square} Test
#on the sample's first digits using defaults
jpsq.benftest(X)
#p-value = 0.3241
``` |

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

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