Benford digit screens

bdig() takes the first nd significant digits of each value. With dp = -1 they are the digits of the shortest decimal that gives back the double, decided exactly, so 0.29 gives 29 where truncating x times a power of ten gives 28; with dp from 0 to 22 the data are taken as recorded to dp decimals. bnft() tests the digits against Benford's law, P(d) = log10(1 + 1 / d), by the chi-square statistic with its exact upper tail, a Monte Carlo p-value from samples of Benford digits of the same size, and Nigrini's mean absolute deviation. A departure from Benford's law is a reason to look, not a finding of fabrication: many honest data sets (bounded amounts, assigned numbers) do not follow it.

Usage

bdig(x, nd = 1, dp = -1, sgn = "pos")

bnft(dig, nd = 1, nsim = 0, seed = NULL)

Arguments

x

Numbers. Zeros, non-finite values (including NA), values of the excluded sign and values outside the exact range are set aside and counted.

nd

The number of leading digits: from 1 to 9 for bdig(), 1 to 6 for bnft().

dp

-1, or the number of decimals the data were recorded to.

sgn

Which values to keep: "pos", "neg" or "both" (by absolute value).

dig

Digits as bdig() returns them (0 is skipped).

nsim

The number of Monte Carlo samples: a whole number from 0.

seed

NULL to draw the simulations' seed from R's generator (so set.seed() fixes them), or one whole number from 0.

Value

bdig(): a list of dig (an integer per value, 0 when set aside) and cnt (zeros, non-finite, excluded sign, out of range). bnft(): a list of obs (a data frame of digit, observed count and Benford expected count) and stat (m digits used, chisq, df, p, pmc (Monte Carlo, NaN without samples) and mad).

References

Benford, F. (1938). The law of anomalous numbers. Proceedings of the American Philosophical Society, 78(4), 551-572.

Nigrini, M. J. (2012). Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud Detection. Wiley. doi:10.1002/9781119203094

Examples

set.seed(1)
x <- exp(runif(500, 0, 10))
d <- bdig(x)$dig
bnft(d, nsim = 199, seed = 1)$stat
#>            m        chisq           df            p          pmc          mad 
#> 500.00000000  15.41054423   8.00000000   0.05163739   0.05000000   0.01580472