Continuous, weighted Lorenz theory and applications to the study of fractional relative impact factors

Abstract

This paper introduces weighted Lorenz curves of a continuous variable, extending the discrete theory as well as the non-weighted continuous model. Using publication scores (in function of time) as the weights and citation scores (in function of time) as the dependent variables, we can construct an “impact Lorenz curve” in which one can read the value of any fractional impact factor, i.e. an impact factor measured at the time that a certain fraction of the citations is obtained or measured at the time a certain fraction of the publications is obtained. General properties of such Lorenz curves are studied and special results are obtained in case the citation age curve and publication growth curve are exponential functions.