On a formula for the h-index

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

“…We shall refer to these formulas as Lambert- W formulas for the h -index, respectively, in a “basic”, , and an “improved” version, . The formula has been considered elsewhere Bertoli-Barsotti and Lando (2015) for the estimation of the h -index for individual scientists.…”

“…In recent years, a certain interest has been shown in developing theoretical models with which to “estimate” one such indicator given the values of certain others. Well-known representative examples are theoretical models with which to obtain the value of the h -index, h :as a function of C (Hirsch 2005),as a function of T (Egghe and Rousseau 2006),as a function of T 1 (Burrell 2013a),as a function of C and T (Glänzel 2006; Iglesias and Pecharroman 2007; Schubert and Glänzel 2007; Bletsas and Sahalos 2009; Egghe et al 2009; Egghe and Rousseau 2012),as a function of C , T 1 and C 1 Bertoli-Barsotti and Lando (2015); but also theoretical models with which to estimate C , as a function of h (Petersen et al 2011), or as a function of m and h (Egghe et al 2009), or as a function of T and h (Burrell 2013b), and so on. These models—usually based, in their turn, on the assumption of a specific probabilistic model for the citation distribution—may be effective, for instance, when the indicator of interest cannot be obtained directly because it is not accessible, or when the availability of citation data is incomplete.…”

“…Recently, Burrell (2013b) and Bertoli-Barsotti and Lando (2015) introduced a model that has proved very effective in estimating the actual value of the h -index for individual scientists. More precisely, 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.…”

“…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.…”

Scientific Production and Productivity in Curriculum Vitae Characterisation: Simple and Nested H Indices that Support Cross-Disciplinary Comparisons

“…For example, indices discussed in recent papers include the c index (Yan et al, 2013), z index (Petersen & Succi, 2013), g index (Adachi & Kongo, 2015;Bartolucci, 2015;Bertoli-Barsotti, 2016;De Visscher, 2011;Prathap, 2014;Rousseau, 2015;Schreiber, 2013a,b), and generalized Hirsch (H) index (Gagolewski & Mesiar, 2012). Here, I will refer to the most popular H index Bertoli-Barsotti & Lando, 2015). In particular, I will calculate alternative nested (as clarified in Section 2) versions of the H index based on common information available in the Scopus dataset, by referring to insights suggested by the authors of other indices and by attempting to solve the empirical shortcomings (e.g., sensitivity to citations, the "fashion" effect, attribution to disciplines, life cycle of articles; Dienes, 2015) as well as the open questions (e.g., the attribution of an article to a given discipline; Gagolewski, 2013) of the original H index.…”