Measuring the citation impact of journals with generalized Lorenz curves

To improve comparisons of journals, which are typically based on single-value indicators,such as the journal impact factor (JIF), this paper proposes a functional approach. We discussinterpretatively three progressively finer dominance relations. The first one correspondsto a comparison between the quantile functions of the citation distributions. The secondone consists in comparing the integrals of the quantile functions—namely, the generalizedLorenz curves (GLCs). The third one consists in comparing the integrals of the GLCs, wherethe integration is designed to emphasize the role of the “central body” of the articles of thejournal. Although dominance relations are generally not complete orders, we demonstratewith an empirical analysis that it is possible to increase significantly the proportion of pairsof journals that are comparable by moving from the first to the second criterion, and thenfrom the second to the third.Because, in practical applications, it may be convenient to reduce such a functional com-parison to a scalar comparison between indicators, we follow an axiomatic approach toidentify classes of indicators that are isotonic with the criteria introduced. We demonstratethat the established JIF may be usefully improved if it is corrected simply by multiplying itby one minus the Gini coefficient. The resulting index, defined as stabilized-JIF, has manyattractive features and it is isotonic with all the dominance relations introduced.