Efficient Estimation of the Lorenz Curve and Associated Inequality Measures from Grouped Observations

Abstract

This paper introduces a new coordinate system for the Lorenz curve.Particular attention is paid to a special case of wide empiricalvalidity. Four alternative methods have been used to estimate theproposed Lorenz curve from the grouped data. The well known inequalitymeasures are obtained as the function of the estimated parametersof the Lorenz curve. In addition the frequency distribution is derivedfrom the equation of the Lorenz curve. An empirical illustrationis presented using the data from the Australian Survey of ConsumerExpenditure and Finances 1967--68.