Monday, October 24, 2011

Benford's law in action

Dow 11,910.82 +102.03 +0.86%
Nasdaq 2,695.27 +57.81 +2.19%
S&P 500 1,253.11 +14.86 +1.20%
10 Yr Bond(%) 2.2260% +0.0230
Oil 91.12 +3.72 +4.26%
Gold 1,650.00 +14.90 +0.91%

All the levels start with mostly 1, and some 2; except for oil, it starts with an improbable 9. One might think the entire economy is a Benford's battle, components just wann have simple numbers!

Funny thin, Benford is maximum entropy, it follows channel theory.
The quantity P(d) is proportional to the space between d and d + 1 on a logarithmic scale. Therefore, this is the distribution expected if the logarithms of the numbers (but not the numbers themselves) are uniformly and randomly distributed.

So the Log(i) is uniform, this is a result if the system is Huffman encoded. To complete the picture, all the -iLog(i) must be within 1.0 to conserve flow. This is maximum entropy channel flow, what is the proper encoding of quants to supply maximum disorder to the channel.

In this case, the components are trying to get their spots in the monetary exchange channel, the fiat thingy. They seek to occupy as much yield curve as possible. Oil seems to be the odd man out.

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