Abstract: In a recent paper, Paul and Shankar (2020) introduced a single-parameter Lorenz curve that provides an improved fit compared to many existing uniparametric models. This paper explores new properties of their model, offering a refined representation in terms of convex linear combinations of Lorenz curves. We also derive closed-form expressions for several inequality measures and examine the Lorenz ordering. However, we identify a key limitation: The Gini index for this curve is lower bounded at 0.418, making the model unsuitable for income distributions with lower inequality. To address this issue, we propose an alternative model that extends the range of the Gini index, allowing for greater flexibility in representing income distributions across a wider range of inequality levels. Our results suggest that the Lorenz curve proposed in this paper surpasses the proposal by Paul and Shankar, even in countries with high inequality, where the constraint imposed by the Gini index is not binding.

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