Bounds and Inequalities Relating h-Index, g-Index, e-Index and Generalized Impact Factor: An Improvement over Existing Models

In this paper, we describe some bounds and inequalities relating [Image: see text]-index, [Image: see text]-index, [Image: see text]-index, and generalized impact factor. We derive the bounds and inequalities relating these indexing parameters from their basic definitions and without assuming any continuous model to be followed by any of them. We verify the theorems using citation data for five Price Medalists. We observe that the lower bound for [Image: see text]-index given by Theorem 2, [Image: see text], comes out to be more accurate as compared to Schubert-Glanzel relation [Image: see text] for a proportionality constant of [Image: see text], where [Image: see text] is the number of citations and [Image: see text] is the number of papers referenced. Also, the values of [Image: see text]-index obtained using Theorem 2 outperform those obtained using Egghe-Liang-Rousseau power law model for the given citation data of Price Medalists. Further, we computed the values of upper bound on [Image: see text]-index given by Theorem 3, [Image: see text], where [Image: see text] denotes the value of [Image: see text]-index. We observe that the upper bound on [Image: see text]-index given by Theorem 3 is reasonably tight for the given citation record of Price Medalists.