digit.distr {BeyondBenford}

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)
digit.distr(address_AixesurVienne,mod="ben&blo",lwbound=2,No.sd=1, Sd.pr=1)

data(address_PierreBuffiere)
digit.distr(address_PierreBuffiere,mod="blo",dig=2)