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Certainty equivalent citation: generalized classes of citation indexes

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Abstract

Drawing from the existing literature on risk and inequality measurement, we implement the notion of “certainty equivalent citation” in order (i) to generalize most of the h-type citation indexes (h-, g-, \(\tilde{g},\) t-, f-, w-index), and (ii) to highlight the centrality of the decision-maker’s preferences on distributive aspects (concentration aversion) for the ranking of citation profiles. In order to highlight the sensitivity of citation orderings with respect to concentration aversion, an application to both simulated and real citation profiles is presented.

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Notes

  1. In this paper we do not consider the indexes complementing the h-index (Jin et al. 2007; Zhang 2009) as well as the re-scaling procedures suggested in order to overcome some of the major cons of the h-index (Katsaros et al. 2006; Batista et al. 2006; Jin et al. 2007; Schreiber 2008; Wu 2010; Ellison 2010; Harzing 2011).

  2. As observed in Woeginger (2008b), the \(\tilde{g}\)-index “seems to give the nicest and most natural version of the g-index”.

  3. It is worth observing that the same issue had already been highlighted with respect to mean and median citation rate metrics in Tijssen (2002) and Aksnes and Sivertsen (2004). More recently, in order to account for the skewness of citation distributions, Leydesdorff et al. (2011) and Leydesdorff and Bornmann (2011) have submitted new indicators based on a percentile rank approach, while a quadratic influence function has been proposed in Ravallion and Wagstaff (2011) by which a preference for “diminishing marginal influence of citations” is additionally assumed.

  4. Equivalently, \(x:=\{x_1,\ldots,x_n\}\) is an element of the non-negative part of the n-dimensional Euclidean space with the origin excluded.

  5. In addition, it must be the case that h(x) ≤ w(x) ≤ 2 h(x) (Woeginger 2008a).

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Authors and Affiliations

  1. Department of Economics and Statistics, University of Salerno, Via Ponte don Melillo 1, 84084, Fisciano, SA, Italy

    Antonio Abatemarco

  2. Department of Business Economics, Legal, Merceological and Geographical Science, University of Foggia, Largo Giovanni Paolo II 1, 71100, Foggia, FG, Italy

    Roberto Dell’Anno

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  1. Antonio Abatemarco
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Correspondence to Antonio Abatemarco.

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Abatemarco, A., Dell’Anno, R. Certainty equivalent citation: generalized classes of citation indexes. Scientometrics 94, 263–271 (2013). https://doi.org/10.1007/s11192-012-0758-x

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