## Hirsch Index Rankings Require Scaling and Higher Moment

### BibTeX

@MISC{Bletsas_hirschindex,

author = {Aggelos Bletsas and John N. Sahalos},

title = {Hirsch Index Rankings Require Scaling and Higher Moment},

year = {}

}

### OpenURL

### Abstract

Abstract: Simple bibliometric indicators, such as average number of citations per publication per researcher, or the recently-proposed Hirsch index (h-index), are nowadays tracked by online repositories including Web-of-Science (WOS) and often affect critical decision making. This work proposes appropriate scaling of the h-index, based on its probability distribution which is calculated for any underlying citation distribution. The proposed approach outperforms existing index estimation models which have focused on the expected value only (i.e. first moment). Furthermore, it is shown that average number of citations per publication per scientific field, total number of publications per researcher, as well as researcher’s h-index measured value, expected value and standard deviation constitute the minimum information required for meaningful h-index ranking campaigns; otherwise contradicting ranking results emerge. This work may potentially shed light to (current or future) large-scale, h-index-based bibliometric evaluations.

### Citations

271 |
An index to quantify an individual's scientific research output
- Hirsch
(Show Context)
Citation Context ...ons per publication per researcher CT / NT, and the recently proposed Hirsch index (h-index for brevity) that depends on number of publications (activity) as well as number of citations (visibility) (=-=Hirsch 2005-=-, 2007); all such information is readily available by commercial databases, such as Thompson Scientific Web-of-Science (WOS) and Elsevier Scopus or can be calculated through other online repositories.... |

155 |
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(Show Context)
Citation Context ...ementary cumulative distribution function Fc(x), expected value E{X} and ordered Yκ’s (defined in Section 2.1). 3 The chosen distributions have been utilized in bibliometrics to model empirical data (=-=Redner, 1998-=-), (Laherrere and Sornette, 1998), (Tsallis and de Albuquerque, 2000). It is further noted that Tsallis distribution is also known as q-exponential distribution or generalized type II Pareto distribut... |

108 |
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(Show Context)
Citation Context ...006), introductory citations without real significance to the presented work, gratuitous authorship, citation coalitions and disproportional citations to widely-known researchers (``Mathew effect'') (=-=Merton, 1968-=-). Furthermore, self-citations in top international journals could reach roughly 50% of the total citations (as observed in this work) and thus, bibliometric indicators should be modified accordingly.... |

81 |
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(Show Context)
Citation Context ...ive distribution function Fc(x), expected value E{X} and ordered Yκ’s (defined in Section 2.1). 3 The chosen distributions have been utilized in bibliometrics to model empirical data (Redner, 1998), (=-=Laherrere and Sornette, 1998-=-), (Tsallis and de Albuquerque, 2000). It is further noted that Tsallis distribution is also known as q-exponential distribution or generalized type II Pareto distribution (Shalizi, 2007 and reference... |

31 | An Informetric Model for the Hirsch Index - Egghe, Rousseau - 2006 |

22 | Are There Better Indices for Evaluation Purposes than the h-index? A Comparison of Nine Different Variants of the h Index Using Data from Biomedicine - Bornmann, Mutz, et al. - 2008 |

15 | Dynamic h-index: The Hirsch Index in Function of Time - Egghe |

15 |
Scaling the h-index for Different Scientific ISI Fields
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(Show Context)
Citation Context ... periods. Similar modelling with Weibull can be found in (Laherrere and Sornette, 1998). It is also remarked that Weibull (also known as Stretched Exponential) was instead used in (Hirsch, 2005) and (=-=Iglesias and Pecharroman, 2007-=-) to model the ordered Yκ’s of Eq. (1) and not the citation distribution itself. Figs. 1, 2 show that the two methods for h-index estimation provide similar results, as expected; the numerical results... |

10 | A case study of the Hirsch index for 26 non-prominent physicists
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(Show Context)
Citation Context ...s nearly half of the total number of citations (CT). This observation needs further investigation and it is coherent with previous studies showing that self-citations considerably affect the h-index (=-=Schreiber, 2007-=-a, 2007b). 4. Ranking challenge 4.1 Measurements 11The study was originally planned to provide rankings of similar-discipline departments mainly in Greece, according to their measured bibliometric in... |

10 |
A Systematic Analysis of Hirsch-type Indices for Journals
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(Show Context)
Citation Context ...lso provides the estimated h-index (hest) for Tsallis with q = 1.6, Weibull with 2 / 3 1/ 3 c = 0.4 and Pareto with b = 0.75 and a = 3 in Eq. (4), providing Ε{ h } = 0. 75( C / N ) N , exactly as in (=-=Schubert and Glänzel, 2007-=-). Thus, one can easily assess the estimation error T T T 9hmeas - hest, for the provided models. 4 Fig. 3 visualizes the absolute estimation error |hmeas - hest| for the above three models, as well ... |

9 | Higher Education Supplement - Times - 2004 |

9 | Hirsch’s h-index: A Stochastic Model - Burrell |

9 |
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(Show Context)
Citation Context ...presentative yardstick compared to the average number of citations per publication for a particular researcher. This observation could explain the statistical uncertainty of the h-index, reported in (=-=Lehmann, Jackson, and Lautrup, 2005-=- and 2006), where it was shown through simple Bayesian inference that un-scaled h-index ranking is as relevant to scientific activity/visibility as ranking according to name-alphabetical order, i.e. i... |

8 |
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(Show Context)
Citation Context ...d be modified accordingly. Relevant corrections of the h-index regarding self-citations (e.g. see work by Schreiber 2007a, 2007b) or multi-authorship (e.g. see work by Chai, Hua, Rousseau, Wan, 2008, =-=Schreiber 2008-=-, Egghe 2008) have already started to appear in the literature. Acknowledgments The authors would like to thank Prof. Stavros Panas, Vice-Rector of Aristotle University of Thessaloniki, for his kind s... |

8 |
Maximum likelihood estimation for q-exponential (Tsallis) distributions
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(Show Context)
Citation Context ...aherrere and Sornette, 1998), (Tsallis and de Albuquerque, 2000). It is further noted that Tsallis distribution is also known as q-exponential distribution or generalized type II Pareto distribution (=-=Shalizi, 2007-=- and references therein), (Burrell, 2008). In order to avoid confusion with the standard Power Law/Pareto distributions, we keep the term ``Tsallis distribution”. As a first example, we calculate the ... |

6 | Does the h index have predictive power - Hirsch |

6 | Rational (successive) h-indices: An application to economics in the Republic of Ireland. Scientometrics - Ruane, Tol - 2008 |

5 |
Mathematical Theory of the h- and g-Index in Case of Fractional Counting of Authorship
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(Show Context)
Citation Context ...cordingly. Relevant corrections of the h-index regarding self-citations (e.g. see work by Schreiber 2007a, 2007b) or multi-authorship (e.g. see work by Chai, Hua, Rousseau, Wan, 2008, Schreiber 2008, =-=Egghe 2008-=-) have already started to appear in the literature. Acknowledgments The authors would like to thank Prof. Stavros Panas, Vice-Rector of Aristotle University of Thessaloniki, for his kind support and a... |

4 |
An empirical investigation of the g-index for 26 physicists in comparison with the h-Index, the Aindex, and the R-index
- Schreiber
- 2008
(Show Context)
Citation Context ...d be modified accordingly. Relevant corrections of the h-index regarding self-citations (e.g. see work by Schreiber 2007a, 2007b) or multi-authorship (e.g. see work by Chai, Hua, Rousseau, Wan, 2008, =-=Schreiber 2008-=-, Egghe 2008) have already started to appear in the literature. Acknowledgments The authors would like to thank Prof. Stavros Panas, Vice-Rector of Aristotle University of Thessaloniki, for his kind s... |

3 | Real and rational variants of the h-index and the g-index - Guns, Rousseau - 2009 |

3 | Measures for measure - Lehmann, Jackson, et al. - 2006 |

2 | The Adapted Pure h-Index - Chai, Hua, et al. - 2008 |

2 | A quantitative analysis of indicators of scientific performance - Lehmann, Jackson, et al. - 2008 |

1 |
Probability distribution, scaling and ranking challenges behind the h-index. RadioCommunications Laboratory (RCL
- Bletsas, Sahalos
- 2008
(Show Context)
Citation Context ...nts. More importantly, the study revealed significant variance in research domains, even among departments of the same discipline e.g. among physics departments or electrical engineering departments (=-=Bletsas and Sahalos, 2008-=-). The dependence of h-index on the citation distribution (or at minimum, on the average citations per publication per field E{X}) emphatically directs additional measurements before any ranking attem... |

1 |
Extending Lotkaian Informetrics
- Burrell
- 2008
(Show Context)
Citation Context ...nd de Albuquerque, 2000). It is further noted that Tsallis distribution is also known as q-exponential distribution or generalized type II Pareto distribution (Shalizi, 2007 and references therein), (=-=Burrell, 2008-=-). In order to avoid confusion with the standard Power Law/Pareto distributions, we keep the term ``Tsallis distribution”. As a first example, we calculate the expected value for the h-index, using th... |

1 | b). Self-citation corrections for the hirsch index - unknown authors - 2007 |

1 |
Do you sincerely want to be cited? Or: read before you cite
- Simkin, Roychowdhury
- 2006
(Show Context)
Citation Context ...g campaigns, providing additional motivation for this work. Future work should focus on multi-parametric methods that alleviate poor practices, such as citing papers that have not been actually read (=-=Simkin and Roychowdhury, 2006-=-), introductory citations without real significance to the presented work, gratuitous authorship, citation coalitions and disproportional citations to widely-known researchers (``Mathew effect'') (Mer... |

1 | Are citations of scientifc papers a case of nonextensivity? Eur - Tsallis, Albuquerque - 2000 |