A CLASS OF LORENZ CURVES BASED ON LINEAR EXPONENTIAL LOSS FUNCTIONS

ABSTRACT

In this paper a new kind of Lorenz curves based on the exponential linear asymmetric loss function is introduced. We shall begin with the basic biparametric curve , and we shall build a hierarchy of Lorenz curves with an increasing number of parameters according to the method proposed by Sarabia, Castillo and Slottje.[1] The family is very flexible and the convexity conditions will be easy to check. A variety of properties are analysed, including Lorenz orderings, population functions and inequality measures. Fitting and estimation methods are proposed. Finally, an application is presented for data from various countries.

Keywords:

• Lorenz curves
• LINEX loss functions
• Hierarchy of Lorenz curves

ACKNOWLEDGMENTS

We thank the Ministerio de Ciencia y Tecnología, project BEC2000-1186, for partial support of this work. Comments by two anonymous referees have improved the paper.