In fat-tailed domains , sample measures of top centile contributions to the total (concentration) are biased, unstable estimators extremely sensitive to  sample size and concave in accounting for large deviations. They can vary over time merely from the increase of sample space , thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as weighted concen- tration measures for A and B will tend to be lower than that from A + B. In addition, it can be shown that under fat tails, increases in the total sum need to be accompanied by increased measurement of concentration. We examine the bias and error under straight and mixed distributions.
In domains with power law tails , sample measures of top centile contributions to the total (concentration) are biased, unstable estimators extremely sensitive to both unit and sample size and concave in accounting for large deviations. They can vary over time merely from the increase of unit size , thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as weighted concentration measures for A and B will tend to be lower than that from A + B. In addition, it can be shown that under fat tails, increases in the total sum need to be accompanied by increased measurement of concentration. We examine the bias and error under straight and mixed distributions.
R
fat-tailed domains
domains with power law tails
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both unit and
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sample space
unit size
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concen- tration
concentration