Benford's Law for first digit

Benford's Law states that the probability that the first digit equals d is approximately the logarithm of (1 + 1/d). By plotting the expected frequencies, it will be clear that the digits 1,…,9 do not occur with equal frequency.

This exercise is part of the course

Fraud Detection in R

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Exercise instructions

Implement Benford's law as a function benlaw for the first digit using log base 10 .
Calculate the expected frequency for having 5 as a first digit.
Create a dataframe with one column digit holding digits from 1 to 9, and one column probability holding their respective probabilities under Benford's Law.
Submit to plot the expected frequencies for the digits 1, 2, …, 9 in a barplot.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Implement Benford's Law for first digit
benlaw <- function(d) log10(___ + ___ / ___)

# Calculate expected frequency for d=5
benlaw(___)

# Create a dataframe of the 9 digits and their Benford's Law probabilities
df <- data.frame(digit = ___:___, probability = ___)

# Create barplot with expected frequencies
ggplot(df, aes(x = digit, y = probability)) + 
	geom_bar(stat = "identity", fill = "dodgerblue") + 
	xlab("First digit") + ylab("Expected frequency") + 
	scale_x_continuous(breaks = 1:9, labels = 1:9) + 
	ylim(0, 0.33) + theme(text = element_text(size = 25))

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