A relative-rank measure for the rank transformation

Abstract

This research introduces a new ranking scheme capable of ordering competing units in a more continual manner. The classic ranks are functionalized by incorporating data range and quantile coverage simultaneously in the proposed formula. This dual use of additional information is found to enhance the sensitivity of the devised scheme towards offering more competent weights of competing observations. Some key mathematical properties of the proposed approach are highlighted. In particular, the capability of the devised approach in offering unambiguous preferences is established. Finally, the performance of the proposed measure is investigated under a set of diverse parametric settings involving different stochastic formulations, sample sizes, and degrees of correlation.