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April 5th, 2019, 01:21 AM   #1
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Comparing Distributions of Datasets

I've been asked to find a method to best compare the distribution of a number datasets that have small sample sizes. Bonus points for a solution/result that is in a scale of 0-1, i.e. a distribution approaching 1 is bordering on perfectly unequal and a distribution approaching 0 is bordering on perfectly equal.

Some examples within this dataset include:
  • Sample A: [10,1]
  • Sample B: [10,1,1]
  • Sample C: [4,4,3,2,2]
In other words, the method used should show A to have a distribution close close to 1 (almost perfectly unevenly distributed), B to be close to 1 but further away from 1 than A's distribution, and C to be closer to 0 (quite an equal distribution).

I first thought of the Gini coefficient, which is precisely about distribution and gives values between 0-1. However it seems the Gini has a 'small-sample bias' that limits its use here, where each of the datapoints have between 1 and c.10 values.

I then considered the coefficient of variance, however given results can go higher than 1 this also isn't well suited to this problem.

Any pointers would be greatly appreciated!
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April 5th, 2019, 01:58 AM   #2
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What about entropy?
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