The Gini coefficient and discontinuity
This article reveals a discontinuity in the mapping from a Lorenz curve to the associated cumulative distribution function. The problem is of a mathematical nature—based on an analysis of the transformation between the distribution function of a bound random variable and its Lorenz curve. It will be...
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2022-12-01
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| Series: | Cogent Economics & Finance |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/23322039.2022.2072451 |
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| Summary: | This article reveals a discontinuity in the mapping from a Lorenz curve to the associated cumulative distribution function. The problem is of a mathematical nature—based on an analysis of the transformation between the distribution function of a bound random variable and its Lorenz curve. It will be proven that the transformation from a normalized income distribution to its Lorenz curve is a continuous bijection with respect to the [Formula: see text] ([0,1])-metric—for every q ≥ 1. The inverse transformation, however, is not continuous for any q ≥ 1. This implies a more careful attitude when interpreting the value of a Gini coefficient. A further problem is that if you have estimated a Lorenz curve from empirical data,then you cannot trust that the associated distribution is a good estimate of the true income distribution. |
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| ISSN: | 2332-2039 |