Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/303649 
Year of Publication: 
2022
Citation: 
[Journal:] Cogent Economics & Finance [ISSN:] 2332-2039 [Volume:] 10 [Issue:] 1 [Article No.:] 2072451 [Year:] 2022 [Pages:] 1-16
Publisher: 
Taylor & Francis, Abingdon
Abstract: 
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 Lq ([0,1])-metric-for every q Ï 1. The inverse transformation, however, is not continuous for any q Ï 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.
Subjects: 
inequality
probability
math analysis
discontinuity
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article

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