digit.distr {BeyondBenford} R Documentation

## Distribution of figures in a given position

### Description

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. Error bars can be added to the plotted histogram.

### Usage

```digit.distr(dat, mod = "ben", lwbound = max(floor(min(abs(dat))) + 1, (10^(dig - 1))),
upbound = ceiling(max(dat)), dig = 1, col = c("#E69F00", "#999999"),
colbl = c("#AAFFAA", "#999999"), colbebl = c("#E69F00", "#AAFFAA", "#999999"),
main = "Distribution of digits", No.sd = 0, Sd.pr = 0)
```

### Arguments

 `dat` The considered dataset, a data frame containing non-zero real numbers. `mod` A character string. 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. `lwbound` A positive integer, which characterizes the data. All (or most) of the data are greater than this "lower bound". `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 two colors used to fill the bars of the histogram, if both the data histogram and Blondeau Da Silva's histogram are plotted. `colbebl` A vector containing three colors used to fill the bars of the histogram, if mod="ben&blo". `main` The title of the graph. `No.sd` The positive decimal number of standard deviation that defines the confidence intervals i.e. the error bars. If No.sd=0, no error bars are drawn. `Sd.pr` If Sd.pr=1, error bars for proportions are plotted (with No.sd standard deviation confidence intervals). If Sd.pr=0, they are not plotted.

### 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.

### Author(s)

Blondeau Da Silva St\'ephane

### References

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

S. Blondeau Da Silva (2020). Benford or not Benford: a systematic but not always well-founded use of an elegant law in experimental fields. Communications in Mathematics and Statistics, 8:167-201. doi: 10.1007/s40304-018-00172-1.

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.

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

### Examples

```data(address_AixesurVienne)