# digit.distr

##### Distribution of figures in a given position

The function returns histograms of distribution of figures in a given position: (i) in the dataset, (ii) due to Benford, (iii) due to Blondeau Da Silva.

##### Usage

```
digit.distr(dat, mod = "ben", upbound = ceiling(max(dat)), dig = 1,
col = c("#FFFFAA", "#AAFFAA"), colbl = c("#FFFFAA", "#AAFFFF"),
colbebl = c("#FFFFAA", "#AAFFAA", "#AAFFFF"), main = "Distribution of digits",
legend = TRUE, leg = c("Observed", "Benford"),
legbebl = c("Observed", "Benford", "Blondeau"), legbl = c("Observed", "Blondeau"))
```

##### Arguments

- dat
The considered dataset, a data frame containing non-zero real numbers.

- mod
If mod="ben", the data histogram and that of Benford are displayed, if mod="ben&blo", the data histogram, that of Benford and that of Blondeau Da Silva are plotted, and otherwise the data histogram and that of Blondeau Da Silva are given.

- upbound
A positive integer, which characterizes the data. All (or most) of the data are lower than this "upper bound".

- dig
The chosen position of the digit (from the left).

- col
A vector containing two colors used to fill the bars of the histogram, if mod="ben".

- colbl
A vector containing three colors used to fill the bars of the histogram, if mod="ben&blo".

- colbebl
A vector containing two colors used to fill the bars of the histogram, if the latter case.

- main
The title of the graph.

- legend
If legend=TRUE, the legend is displayed.

- leg
A two-components vector containing text appearing in the legend, if mod="ben".

- legbebl
A three-components vector containing text appearing in the legend, if mod="ben&blo".

- legbl
A two-components vector containing text appearing in the legend, if the latter case.

##### Value

Histograms of distribution of figures in a given position: (i) in the dataset, (ii) due to Benford, (iii) due to Blondeau Da Silva.

##### Note

This warning message can appear: NAs introduced during the automatic conversion. This is due to the fact that some data are not numerical in the entered dataset. Non numerical values and zeros are not counted.

##### References

F. Benford (1938). The law of anomalous numbers. Proceedings of the American Philosophical Society, 78:127-131.

S. Blondeau Da Silva (2018). Benford or not Benford: a systematic but not always well-founded use of an elegant law in experimental fields. https://arxiv.org/abs/1804.06186.

S. Blondeau Da Silva (2018). Benford or not Benford: new results on digits beyond the first. https://arxiv.org/abs/1805.01291.

T. Hill (1995). The significant-digit phenomenon. The American Mathematical Monthly, 102(4):322-327. 10.2307/2974952.

R. Newcomb (1881). Note on the frequency of use of the different digits in natural numbers. American Journal of Mathematics, 4:39-40. 10.2307/2369148.

##### Examples

```
# NOT RUN {
data(address_AixesurVienne)
digit.distr(address_AixesurVienne,mod="ben&blo",upbound=75)
data(address_PierreBuffiere)
digit.distr(address_PierreBuffiere,mod="blo",dig=2)
# }
```

*Documentation reproduced from package BeyondBenford, version 1.0, License: GPL-2*