A relation between h-index and impact factor in the power-law model

A theoretical model of the relationship between the h-index and other simple citation indicators

Of the existing theoretical formulas for the h-index, those recently suggested by Burrell (J Informetr 7:774-783, 2013b) and by Bertoli-Barsotti and Lando (J Informetr 9(4):762-776, 2015) have proved very effective in estimating the actual value of the h-index Hirsch (Proc Natl Acad Sci USA 102:16569-16572, 2005), at least at the level of the individual scientist. These approaches lead (or may lead) to two slightly different formulas, being based, respectively, on a "standard" and a "shifted" version of the geometric distribution. In this paper, we review the genesis of these two formulas-which we shall call the "basic" and "improved" Lambert-W formula for the h-index-and compare their effectiveness with that of a number of instances taken from the well-known Glänzel-Schubert class of models for the h-index (based, instead, on a Paretian model) by means of an empirical study. All the formulas considered in the comparison are "ready-to-use", i.e., functions of simple citation indicators such as: the total number of publications; the total number of citations; the total number of cited paper; the number of citations of the most cited paper. The empirical study is based on citation data obtained from two different sets of journals belonging to two different scientific fields: more specifically, 231 journals from the area of "Statistics and Mathematical Methods" and 100 journals from the area of "Economics, Econometrics and Finance", totaling almost 100,000 and 20,000 publications, respectively. The citation data refer to different publication/citation time windows, different types of "citable" documents, and alternative approaches to the analysis of the citation process ("prospective" and "retrospective"). We conclude that, especially in its improved version, the Lambert-W formula for the h-index provides a quite robust and effective ready-to-use rule that should be preferred to other known formulas if one's goal is (simply) to derive a reliable estimate of the h-index.

A proposal for a novel impact factor as an alternative to the JCR impact factor

One disadvantage of the JCR impact factor, the most commonly used assessment tool for ranking and evaluating scientific journals, is its inability in distinguishing among different shapes of citation distribution curves, leading to unfair evaluation of journals in some cases. This paper aims to put forward an alternative impact factor (IF′) that can properly reflect citation distributions. The two impact factors are linearly and positively correlated, and have roughly the same order of magnitude. Because of the ability of IF′ in distinguishing among different shapes of citation distribution curves, IF′ may properly reflect the academic performance of a scientific journal in a way that is different from the JCR impact factor with some unique features that reward journals with highly cited papers. Therefore, it is suggested that IF′ could be used to complement the JCR impact factor.

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 -index, -index, -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 -index given by Theorem 2, , comes out to be more accurate as compared to Schubert-Glanzel relation for a proportionality constant of , where is the number of citations and is the number of papers referenced. Also, the values of -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 -index given by Theorem 3, , where denotes the value of -index. We observe that the upper bound on -index given by Theorem 3 is reasonably tight for the given citation record of Price Medalists.