# Benford’s Law: Futility or Utility? from Rocky Humbert

February 17, 2012 |

SpecListers occasionally report on novel sightings of Benford's Law — both its utility and its futility.

The latest sighting is from a Journal of the Physics Society, where Mr. T.A. Mir at the Nuclear Research Laboratory, Astrophysical Sciences Division in Kashmir, India evidently had too much time (and yellow cake) on his hands, and set aside his quarks to ponder "The Leading Digit Distribution of the Worldwide Illicit Financial Flows." (sic)

The paper (which I didn't read because of poor grammar in the title) can be found here.

Not to be outdone by a physicist (an EXPERIMENTAL one, no less), I just ran the Benford's Law distribution on the monthly CPI data from both the USA and China for the last umpteen years.

Here's the distribution (using the leading digit to the right of the decimal point, since the digit to the left of the decimal is almost always zero hence I used my poetic license to move the decimal point one place to the right.):

China:

0: 8%

1: 19%

2: 17%

3: 21%

4: 11%

5: 14%

6: 13%

7: 15%

8: 11%

9: 14%

USA:

0: 8%

1: 19%

2: 21%

3: 15%

4: 22%

5: 17%

6: 18%

7: 19%

8: 11%

9: 12% (Percents don't equal 100 due to rounding.)

As any self-respecting THEORETICAL physicist can tell you, the appropriate Benford distribution should be

1: 30.1%

2: 17.6%

3: 12.5%

4: 9.7%

5: 7.9%

6: 6.7%

7: 5.8%

8: 5.1%

9: 4.6%

Alas, Mr. Benford lived in the universe of Natural Numbers and not the more restrictive Whole Number world, (which is a mathematically imprecise way of saying that he ain't got no zeros.) So, I'll take some liberty and add all of the zeros to the ones (since that's allowed using the core principle known as "Close Enough For Government Work." ) But even after I do that, it's not Benford-esque. It's much closer to a uniform distribution. So — there you have it: In 10 minutes on a boring afternoon, based on the inspiration of an EXPERIMENTAL nuclear physicist on the other side of the world, I just proved that both the USA and the Chinese are lying about their respective CPI's. Only one question remains: Will ZEROHEDGE pick up this startling conclusion and run with it?

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