An econometric property of the g-index

Let X = (x1, …, xN) and Y = (y1, …, yN  ) be two decreasing vectors with positive coordinates such that ∑j=1Nxj=∑j=1Nyj (representing e.g. citation data of articles of two authors or journals with the same number of publications and the same number of citations (in total)). It is remarked that if the Lorenz curve L(X) of X is above the Lorenz curve L(Y) of Y, then the g-index g(X) of X is larger than or equal to the g-index g(Y) of Y. We indicate that this is a good property for so-called impact measures which is not shared by other impact measures such as the h-index. If L(X) = L(Y  ) and ∑j=1Nxj>∑j=1Nyj we prove that g(X) ⩾ g(Y). We can even show that g(X) > g(Y) in case of integer values xi and yi and we also investigate this property for other impact measures.