A Class of Lorenz Curves Based on Linear Exponential Loss Functions

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] Sarabia, J.M., Castillo, E. and Slottje, D.J. 1999. An Ordered Family of Lorenz Curves. Journal of Econometrics, 91: 43–60. [Crossref], [Web of Science ®] , [Google Scholar] 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.