How mean rank and mean size may determine the generalised Lorenz curve: With application to citation analysis

Abstract

Within the wide framework of information production processes, we present a conversion formula that expresses the generalised Lorenz (GL) curve of a size-frequency distribution as a function of the corresponding rank-size distribution using a fully discrete modelling approach. Based on this conversion formula, we introduce a somewhat universal model for the GL curve of the empirical size-frequency distribution. This study's approach to determining the GL curve is indirect, as we obtain our model for the size-frequency framework by modelling the rank-size distribution and not by directly modelling the size distribution or the GL curve itself, as is usually done. Our GL curve model is particularly appealing because it provides a simple and economical description of the distribution that depends on only three quantities: the (i) mean size, (ii) mean rank, and (iii) maximal rank. The model's performance in predicting the shape of the empirical GL curve is illustrated through a case study involving citation analysis.