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Distorted Lorenz curves: models and comparisons

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Abstract

The economic literature contains many parametric models for the Lorenz curve. A number of these models can be obtained by distorting an original Lorenz curve \(L\) by a function \(h\), giving rise to a distorted Lorenz curve \({\widetilde{L}}=h\circ L\). In this paper, we study, in a unified framework, this family of curves. First, we explore the role of these curves in the context of the axiomatic structure of Aaberge (2001) for orderings on the set of Lorenz curves. Then, we describe some particular models and investigate how changes in the parameters in the baseline Lorenz curve \(L\) affect the transformed curve \({\widetilde{L}}\). Our results are stated in terms of preservation of some stochastic orders between two Lorenz curves when both are distorted by a common function.

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Acknowledgments

We are grateful for the constructive suggestions provided by the reviewers and the Associate Editor, which improved the paper. Miguel A. Sordo is partially supported by Ministerio de Ciencia e Innovación (Grant MTM2009-08326) and Consejería de Economía, Innovación, Ciencia y Empleo (Grant P09-SEJ-4739). Jorge Navarro is partially supported by Ministerio de Ciencia y Tecnología de España (Grant MTM2009-08311) and Fundación Séneca (C.A.R.M.) under Grant 08627/PI/08. José M. Sarabia is partially supported by Ministerio de Economía y Competitividad (project ECO2010-15455).

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Authors and Affiliations

  1. Department of Statistics and OR, University of Cádiz, Cádiz, Spain

    Miguel A. Sordo

  2. Department of Statistics and OR, University of Murcia, Murcia, Spain

    Jorge Navarro

  3. Department of Economics, University of Cantabria, Santander, Spain

    José María Sarabia

Authors
  1. Miguel A. Sordo
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  2. Jorge Navarro
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  3. José María Sarabia
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Correspondence to Miguel A. Sordo.

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Sordo, M.A., Navarro, J. & Sarabia, J.M. Distorted Lorenz curves: models and comparisons. Soc Choice Welf 42, 761–780 (2014). https://doi.org/10.1007/s00355-013-0754-y

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