On Stochastic Ordering and a General Class of Poverty Indexes

Abstract

Although measures of diversity and inequality have been extensively proposed in socio-economic and health perspectives, violation of a subtle monotonicity criterion (under stochastic ordering) diminishes their rationality and utility in the context of poverty and other ecomomic indexes. A modification is proposed here to develop certain stochastic ordering monotonicity preserving diversity measures that overcome this drawback. Such measures are shown to be invariant under increasing transformation, and thereby appropriate for (partially) ordered categorical response data models. AMS{2000) Subject Classification: 62H17, 62-07.