询问 R EN 中的本福德定律

# load the required packages
require(reshape)
require(stringr)
require(plyr)
require(ggplot2)
require(scales)

# load in data from CSV file
fraudDetection <- read.csv("Fraud Case in Arizona 1993.csv")
names(fraudDetection)

# take only the columns containing the counts and manipulate the data into a "long" format with only one value per row
# let's try to compare the amount of the fraudulent transactions against the Benford's Law
fraudDetection <- melt(fraudDetection["Amount"])

# add columns containing the first and last digits, extracted using regular expressions
fraudDetection <- ddply(fraudDetection, .(variable), transform, first.digit = str_extract(value, "[123456789]"), last.digit  = str_extract(value, "[[:digit:]]$"))

# compare counts of each actual first digit against the counts predicted by Benford’s Law
first_digit_counts <- as.vector(table(fraudDetection$first.digit))
first_digit_actual_vs_expected <- data.frame(
digit            = 1:9,
actual.count     = first_digit_counts,    
actual.fraction  = first_digit_counts / nrow(fraudDetection),
benford.fraction = log10(1 + 1 / (1:9))
)