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A method for estimating lorenz curves
Authors:Enrique Castillo  Ali S Hadi  José María Sarabia
Institution:1. Department of Applied Mathematics and Computational Sciences , University of Cantabria , Santander, 39005, Spain;2. Department of Statistical Sciences , Cornell University , 358 Ives Hall, Ithaca, NY, 14853-3901, USA;3. Department of Economics , University of Cantabria , Santander, 39005, Spain
Abstract:This paper proposes a new method for estimating the parameters of Lorenz Curves (LC’s) and fitting LC’s to observed data. The method is very general. It is applicable to any family of LC’s as long as it is given in closed form which is often the case in practice. The method can also be applied to either the LC or to its associated distribution. The estimators are easy to compute as they are obtained one at a time by solving only one equation in one unknown and in many cases the solutions are given in closed-forms. An additional advantage, that is not shared with the currently used method of estimation, is that the method is invariant as to the specification of which variable is written as a function of the other in the LC form. The method is applied to the most commonly suggested LC’s families. An example of real-life data is used to illustrate the methodology. A simulation study is performed to study the properties of the proposed estimators and to compare them with existing ones. The results seem to indicate that the proposed estimators have good properties and they often perform much better than the existing ones.
Keywords:Elemental percentile method  Gini index  Income inequality measures  Non-linear least-squares  Parameter estimation  Pareto distribution  Pietra index  Robust estimation  Spanish Family Income
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