On a Distance Function-Based Inequality Measure in the Spirit of the Bonferroni and Gini Indices

A natural way of viewing an inequality or a poverty measure is in terms of the vector distance between an actual (empirical) distribution of incomes and some appropriately normative distribution (reflecting a perfectly equal distribution of incomes, or a distribution with the smallest mean that is compatible with a complete absence of poverty). Real analysis offers a number of distance functions to choose from. In this paper, the employment of what in the literature is known as the Canberra distance function leads to an inequality measure in the tradition of the Bonferroni and Gini indices of inequality. The paper discusses some properties of the measure, and presents a graphical representation of inequality which shares commonalities with the well known Lorenz curve depiction of distributional inequality.