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A general method for generating parametric Lorenz and Leimkuhler curves

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  • Sarabia, José María
  • Gómez-Déniz, Emilio
  • Sarabia, María
  • Prieto, Faustino

Abstract

Let L0 consider an initial Lorenz curve. In this paper we propose a general methodology for obtaining new classes of parametric Lorenz or Leimkuhler curves that contain the original curve as limiting or special case. The new classes introduce additional parameters in the original family, providing more flexibility for the new families. The new classes are built from an ordered sequence of power Lorenz curves, assuming that the powers are distributed according to some convenient discrete random variable. Using this method we obtain many of the families proposed in the literature, including the classical proposal of Bradford (1934), Kakwani and Podder (1973) and others. We obtain some inequality measures and population functions for the proposed families.

Suggested Citation

  • Sarabia, José María & Gómez-Déniz, Emilio & Sarabia, María & Prieto, Faustino, 2010. "A general method for generating parametric Lorenz and Leimkuhler curves," Journal of Informetrics, Elsevier, vol. 4(4), pages 524-539.
    • Handle: RePEc:eee:infome:v:4:y:2010:i:4:p:524-539
    DOI: 10.1016/j.joi.2010.06.002
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    2. Unnikrishnan Nair, N. & Vineshkumar, B., 2022. "Modelling informetric data using quantile functions," Journal of Informetrics, Elsevier, vol. 16(2).
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    4. N. Nair & P. Sankaran & S. Sunoj, 2013. "Quantile based stop-loss transform and its applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(2), pages 167-182, June.
    5. Barry C. Arnold & José María Sarabia, 2018. "Analytic Expressions for Multivariate Lorenz Surfaces," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 84-111, December.
    6. E. Gómez-Déniz, 2016. "A family of arctan Lorenz curves," Empirical Economics, Springer, vol. 51(3), pages 1215-1233, November.
    7. Valero, Jordi & Pérez-Casany, Marta & Duarte-López, Ariel, 2022. "The Zipf-Polylog distribution: Modeling human interactions through social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).

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