Drawing the Lorenz Curve and Calculating the Gini Concentration Index from Grouped Data by Computer

• Published in: Oxford bulletin of economics and statistics Vol. 46; no. 3; pp. 273 - 78
• Main Authors: Mazzarino, G, Brown, J A C
• Format: Journal Article
• Language: English
• Published: Oxford Department of Economics, University of Oxford 01.08.1984; Basil Blackwell; Blackwell Publishing Ltd
• Series: Oxford Bulletin of Economics and Statistics
• Subjects: Algorithms; Economic theory; Lorenz Curve; Statistical methods
• ISSN: 0305-9049; 1468-0084

The Lorenz curve is still widely employed by economists to represent the distribution of an essentially positive variate when emphasis is placed on its degree of concentration rather than its location. Despite its limitations, the curve is valued for its 3 main properties: 1. It requires no explicit assumption as to the mathematical form of the underlying frequency distribution. 2. It is unaffected by a scalar transformation of the variate. 3. It leads directly to the Gini index of concentration. An attempt is made to draw the Lorenz curve and calculate the Gini concentration index from grouped data using a computer. The approach taken is one of mathematical interpolation; that is, the data points are taken as given and as not subject to sampling error. An algorithm is presented for drawing the curve through the given points with no knowledge of the underlying function, while still requiring conformation to the rules that govern all Lorenz curves. The algorithm is then submitted to 2 empirical tests.