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Interpolating the Lorenz Curve: Methods to Preserve Shape and Remain Consistent with the Concentration Curves for Components

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  • Masato Okamoto

Abstract

type="main"> C-class interpolation methods that preserve monotonicity and convexity and are thus suitable for the estimation of the Lorenz curve from grouped data are not widely known. Instead, parametric models are usually applied for such estimation. Parametric models, however, have difficulty in accurately approximating every part of income/expenditure distributions. This paper proposes two types of C-class shape-preserving interpolation methods. One is a piecewise rational polynomial interpolation (proposed independently by Stineman and Delbourgo) that enables consistent interpolation of the concentration curves for income/expenditure components, attaining approximately the same accuracy as that of the existing methods when applied to decile-grouped data or to more detailed aggregation. Another is a Hybrid interpolation that employs pieces of curves derived from parametric models on end intervals. Empirical comparisons show that the Hybrid interpolation (with the assistance of parametric models for class-boundary estimation) outperforms the existing methods even when applied to quintile-grouped data without class boundaries.

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  • Masato Okamoto, 2014. "Interpolating the Lorenz Curve: Methods to Preserve Shape and Remain Consistent with the Concentration Curves for Components," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(2), pages 349-384, June.
    • Handle: RePEc:bla:revinw:v:60:y:2014:i:2:p:349-384
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    1. Songpu Shang & Songhao Shang, 2021. "Estimating Gini Coefficient from Grouped Data Based on Shape-Preserving Cubic Hermite Interpolation of Lorenz Curve," Mathematics, MDPI, vol. 9(20), pages 1-11, October.

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