Results for “benford's law”
3 found

Deviations from Benford’s Law over time, in U.S. accounting data

Jialan Wang writes:

So according to Benford’s law, accounting statements are getting less and less representative of what’s really going on inside of companies.  The major reform that was passed after Enron and other major accounting standards barely made a dent.

There is much more at the link.  If you are new to the party, Benford’s Law is that:

…in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 about 30% of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than 5% of the time. This distribution of first digits is the same as the widths of gridlines on the logarithmic scale.

There is more at the link or more here.  Here are two previous MR posts on Benford’s Law.

Greece and Benford’s Law

To detect manipulations or fraud in accounting data, auditors have successfully used Benford’s law as part of their fraud detection processes. Benford’s law proposes a distribution for first digits of numbers in naturally occurring data. Government accounting and statistics are similar in nature to financial accounting. In the European Union (EU), there is pressure to comply with the Stability and Growth Pact criteria. Therefore, like firms, governments might try to make their economic situation seem better. In this paper, we use a Benford test to investigate the quality of macroeconomic data relevant to the deficit criteria reported to Eurostat by the EU member states. We find that the data reported by Greece shows the greatest deviation from Benford’s law among all euro states.

The full article is here, hat tip goes to Chris F. Masse.

How do numbers begin?

In many data series a surprising number of entries begin with the number 1, and the number 2 is also more common than a random distribution might suggest.  This is called Benford’s Law.  For instance about one third of all house numbers start with one.  That may be a quirk of bureaucratic numbering psychology, but the principle also applies to the Dow Jones index history, size of files stored on a PC, the length
of the world’s rivers, and the numbers in newspapers’ front page headlines.  It does not apply to lottery-winning numbers, see the graph at the above link.  Here is an exact statement of the law:

Besides the number 1 consistently appearing
about 1/3 of the time, number 2 appears with a frequency of 17.6%,
number 3 at 12.5%, on down to number 9 at 4.6%.  In mathematical terms,
this logarithmic law is written as F(d) = log[1 + (1/d)], where F is
the frequency and d is the digit in question.

I feel as if someone is pulling my leg.  And I keep thinking of nominal interest rates being bounded from below at zero.  Yes this has practical implications:

…because a year’s accounting data of a company
should fulfill the law, economists can detect falsified data, which is
very hard to manipulate to follow the law. (Interestingly, scientists
found that numbers 5 and 6, rather than 1, are the most prevalent,
suggesting that forgers try to “hide” data in the middle.)

The law was first discovered by an economist (and astronomer), Simon Newcomb.  Here is Wikipedia on the law.  Here is more startling data on where the law applies.  From a completely orthogonal but I suspect not totally irrelevant direction, here is Tim Harford on price stickiness.

This whole topic makes me feel like an idiot for even bringing it up, with apologies to Pythagoras.