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.
Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators , extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators can vary over time and increase with the population size, as shown in this article, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as the weighted average of concentration measures for A and B will tend to be lower than that from A U B. In addition, it can be shown that under such fat tails, increases in the total sum need to be accompanied by increased sample size of the concentration measurement . We examine the estimation superadditivity and bias under homogeneous and mixed distributions.
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In domains with power law tails, sample
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downward
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,
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both unit and
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They
It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators
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merely from the increase of unit size,
and increase with the population size, as shown in this article,
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weighted
the weighted average of
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+
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such
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measurement of concentration
sample size of the concentration measurement
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bias and error under straight
estimation superadditivity and bias under homogeneous