Journal of Statistics: Advances in Theory and ApplicationsAuthor's: T. H. Abouelmagd and A. A. E. Ahmed
Pages: [221] - [234]
Received Date: December 21, 2015
Submitted by:
DOI: http://dx.doi.org/10.18642/jsata_7100121604
The Lorenz curve is a tool used to represent income distributions: It tells us which proportion of total income is in the hands of a given percentage of population. While, Butler and McDonald [4] and [5] presented a very broad family of distributions for measuring inequality based on incomplete moments. Lorenz curve can be considered an example of incomplete moment of the income distribution for measuring inequality, where Lorenz curve is the first member of this family; it is obtained from this family, when r is equal one. In this article, we study the features of Lorenz curve and the higher orders of Butler-McDonald family and compare among them. In addition, we study Lorenz curve and Butler-McDonald measures under Pareto distribution. Finally, we use a real data of Egyptian income, and consumption to prove that Lorenz curve gives more accurate estimation of income and consumption inequality than higher orders of Butler-McDonald family.
Lorenz curve, Gini coefficient, Bulter-McDonald measure, income and consumption inequality, and Pareto distribution.
