Poverty Measures as Normalized Distance Functions

One rather simple and straightforward way of interpreting a poverty measure is in terms of the ratio of the vector distance between, one the one hand, an actual distribution of incomes and an ideal distribution without any poverty, to the vector distance between a distribution representing complete poverty and the no-poverty distribution, on the other. One can derive alternative poverty measures, with alternative sets of properties, for alternative specifications of the relevant distance function. In this paper, two families of poverty measures have been derived, pursuing this ‘distance function interpretation’ of a poverty measure. One family is based on the Minkowski distance functions of order a, and the other family is based on a generalization of the Canberra distance function. The properties of these families of indices are reviewed, and their relationship with poverty measures that have already been advanced in the literature is identified. The paper aims to advance both a useful interpretation and a useful addition to the stock of known poverty measures.