John Halleck's Proportional Distributions:

Proportional Distribution Overview

We are going to need to know how to proportionaly distribute something. This is a technique related to weighted averages, but not quite the same.

Proportional Distribution

Assume we have a data value D we want to distribute into N bins, and that each bin has a measure associated with it (M1, M2, M3, ... MN) and we want the total to be split up proportional to each measure.

The amount going into bin X is then just:

X = [MX / (M1 + M2 + M3 + ... + MN)] * D

If there is only one bin, then it gets everything, because

bin1 gets  (M1 / M1) * D

One dimensional example

If we have two bins, and bin one has a measure of 10 and bin two has a measure 20, then the amount of a value into each bin is:

bin1 = (10 / (10+20)) * D = (10/30) * D = 1/3 * D =   D/3
bin2 = (20 / (10+20)) * D = (20/30) * D = 2/3 * D = 2*D/3

Or in other words bin1 gets 1/3 of the total and bin 2 gets 2/3. This agrees with most people's intuition that bin two should get twice as much as bin one based on the measures.

Three dimensional version

If we have a three dimensional value, then we have a three dimensional measure. (This is similar to what we saw in the Weighted Averages chapter.)

This measure says not only how much important each coordinate is, but also how the coordinates are related.

In three dimensions the basic equation is still:

X = [ MX / (M1 + M2 + M3 + ... + MN)] * D

But now the individual items are matrices instead of simple numbers, and the operations are now the matrix operations. But the equation remains the same.

What's this good for?

Later we will see how one can adjust networks. Very often when a network is adjusted you have data values for certain points in the network, and the information on surveys that connected those points. Since you know the where the end points of the survey should be, and the survey is likely to not be exactly the right size to fit, we just distribute the difference between the two points proportional to the variance.

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