BeyondBenford (version 1.4)

digit.distr: 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.

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. 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

# NOT RUN {
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)
# }