Thursday, January 27, 2011

My first try at the quantized general yield curve

Maximum entropy economic yield curve

My strategy was to put the Shannon equation equivalent into the black body equation.  My result above.
- the average arrival rate of the ith  channel component, Qi is the cargo size in bits of the ith channel component,
- Natural base,  B - total channel bandwidth, n - number channel components, the width of our equivalent encoder tree
- Converts from bits to nats, the Euler equivalent of a bit

This is the first shot, like to be wrong on some accounts.

The bandwidth, B, of the the curve is the rate at which the goods can be moved in congestion without concern for maintaining quantization.  It should be the point where the curve meets the noise floor.  The bit is the smallest unit of stuff sold for the given channel.There is likely an error in this related to time, rates really would be relative to base rate, B. B is in Htz, but could be converted into the unit of smallest good.

For Q we have no direct computation except by the 'incidence algebra' of the Huffman encoder.  Its value is squared to give me signal power. n should be the longest length of the encoding tree, known as the rank.  The units of Q are nats, the Euler equivalent of the smallest consumer good, say an item from Dollar Tree.

The output should be interpreted as the amount of noise the yield curve should accommodate to insure no inventory goes to zero.  The result probably should be rooted unless the yield curve is in power units.

This equation might be used for a fairly independent sector, like oil or maybe shoelaces or bankers.  To use this, one needs to isolate the entire set of production chain for the particular good, for example, the bales of cotton, the rolls of twine, the assembly, and retail of shoelaces.  They are all treated as an ensemble of trades taken together generate a shoelace into the household inventory.

Q, as a formula, is determined by the optimum selection components in a sum that fits a constricted channel. The mathematicians are supposed to deliver that next month.

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