Bivariate Lorenz curves: a review of recent proposals

• Sarabia, José María ^[1] ; Jordá, Vanesa ^[1]
  1. [1] Universidad de Cantabria

     Universidad de Cantabria

     Santander, España

     
• Localización: Anales de ASEPUMA, ISSN-e 2171-892X, Nº. 22, 2014
• Idioma: inglés
• Enlaces
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• Dialnet Métricas: 1 Cita
• Resumen
  • español

    La extensión de la curva de Lorenz al caso bidimensional y a dimensiones superiores a dos no es un problema trivial. Existen en la literatura tres propuestas de curvas de Lorenz bidimensionales. La primera de estas definiciones fue propuesta por Taguchi (1972a,b). A continuación Arnold (1983) estableció una segunda definición, que es una extensión natural de la curva de concentración. Esta definición no ha recibido mucha atención en la literatura económica. Finalmente, Koshevoy y Mosler (1996) introdujeron la tercera de las definiciones, haciendo uso del concepto de zonoide. Recientemente, Sarabia y Jord´a (2013, 2014) han propuesto varias clases paramétricas de curvas de Lorenz bivariadas haciendo uso de la definici´on de Arnold.

    En el presente trabajo se revisan estas tres definiciones. Se estudia el origen de cada una de ellas, así como sus principales propiedades. Para el caso de la curva de Arnold, se presentan algunas formas paramétricas propuestas para el caso bidimensional, con diferentes estructuras de dependencia y diferentes tipos de marginales. El trabajo termina comentando las extensiones de estas familias a dimensiones superiores a dos, y sus aplicaciones al estudio del bienestar considerando de forma conjunta varios atributos.

  • English

    The extension of the Lorenz curve to the bidimensional case and dimensions higher than two is not trivial. Three different proposals can be found in the liter-ature. The first definition was proposed by Taguchi (1972a,b). Thereafter, Arnold (1983) developed a second definition which was a natural extension of the concentra-tion curve. This proposal has not received much attention in the economic literature. Finally, Koshevoy and Mosler (1996) introduced the third definition using the con-cept of Lorenz Zonoid. Recently, Sarabia and Jord´a (2013, 2014) proposed a number of parametric classes of bivariate Lorenz curves based on the Arnold’s definition.

    In this paper, the three existing definitions are revisited. We investigate their origin as well as the main properties of each of them. In the case of the Arnold’s definition, some parametric forms are presented for the bivariate case with different dependence structures and different marginals. We finish this work by examining briefly the extension of these families to dimensions higher than two and describing their applications to well-being data when several attributes are jointly considered.

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