TOP-curves

Several characteristics of classical Lorenz curves make them unsuitable for the study of a group of top-performers. TOP-curves, defined as a kind of mirror image of TIP-curves used in poverty studies, are shown to possess the properties necessary for adequate empirical ranking of various data arrays, based on the properties of the highest performers (i.e., the core). TOP-curves and essential TOP-curves, also introduced in this article, simultaneously represent the incidence, intensity, and inequality among the top. It is shown that TOP-dominance partial order, introduced in this article, is stronger than Lorenz dominance order. In this way, this article contributes to the study of cores, a central issue in applied informetrics.