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measure of the output's scientific value or impact. Formally, the Hirsch index of an output x is the maximum number h of papers in x having at least h citations each. For instance, if x is the output consisting of one paper that is cited ten
Abstract
The paper pursues the rigorous mathematical study of the Hirsch index and shows that it has power law upper tail distribution and determines the exponent provided that the underlying publication and citation distributions have fat tails as well. The result is demonstrated on the distribution of the Hirsch index of journals. The paper is concluded with some further remarks on the Hirsch index.
Abstract
The Hirsch index is a number that synthesizes a researcher’s output. It is defined as the maximum number h such that the researcher has h papers with at least h citations each. Woeginger (Math Soc Sci 56: 224–232, 2008a; J Informetr 2: 298–303, 2008b) suggests two axiomatic characterizations of the Hirsch index using monotonicity as one of the axioms. This note suggests three characterizations without adopting the monotonicity axiom.
Summary
The h-index (or Hirsch-index) was defined by Hirsch in 2005 as the number h such that, for a general group of papers, h papers received at least h citations while the other papers received no more than h citations. This definition is extended here to the general framework of Information Production Processes (IPPs), using a source-item terminology. It is further shown that in each practical situation an IPP always has a unique h-index. In Lotkaian systems h = T 1 / a , where T is the total number of sources and α is the Lotka exponent. The relation between h and the total number of items is highlighted.
introduction of h index by Hirsch ( 2005 ) has provided enormous impetus in finding tools to quantify the research output of individual scientists, university faculties and research institutions. The Hirsch index h is defined as the highest number of papers
Abstract
It appears popular, particularly among science administrators, to use citations and various citation measures for ranking scientists, as if such exercises would reflect the scientific potential of the persons considered. In recent time the Hirsch index h in particular has obtained visibility in this respect in view of its simplicity. We consider a possible extension of the concept of selective citations, which in fact is innate to the h index, and propose a simple generalization, indices H and Q, which to a degree supplement the information accompanying the evaluation of h. The H index keeps record of the “history” of citations and the quotient Q = H/h is a measure for the quality of a scientist based on the history of his/her citations.
Summary
An interesting twist of the Hirsch index is given, in terms of an index for topics and compounds. By comparing both the hb index and m for a number of compounds and topics, it can be used to differentiate between a new so-called hot topic with older topics. This quick method is shown to help new comers to identify how much interest and work has already been achieved in their chosen area of research.
Abstract
The authors present ranked lists of world’s countries — with main focus on EU countries (together with newly acceeded and candidate countries) — by their h-index on various science fields. As main source of data Thomson Scientific’s Essential Science Indicators (ESI) database was used. EU countries have strong positions in each field but none of them can successfully compete with the USA. The modest position of the newly accessed and candidate countries illustrate the importance of supportive economic and political background in order to achieve scientific success. An attempt is made to fit a recent theoretical model relating the h-index with two traditional scientometric indicators: the number of publications and the mean citation rate.
Abstract
Hirsch’s h-index gives a single number that in some sense summarizes an author’s research output and its impact. Since an individual author’s h-index will be time-dependent, we propose instead the h-rate which, according to theory, is (almost) constant. We re-analyse a previously published data set (Liang, 2006) which, although not of the precise form to properly test our model, reveals that in many cases we do not have a constant h-rate. On the other hand this then suggests ways in which deeper scientometric investigations could be carried out. This work should be viewed as complementary to that of Liang (2006).
In this paper we present characteristics of the statistical correlation between the Hirsch (h-) index and several standard bibliometric indicators, as well as with the results of peer review judgment. We use the results of a large evaluation study of 147 university chemistry research groups in the Netherlands covering the work of about 700 senior researchers during the period 1991-2000. Thus, we deal with research groups rather than individual scientists, as we consider the research group as the most important work floor unit in research, particularly in the natural sciences. Furthermore, we restrict the citation period to a three-year window instead of 'life time counts' in order to focus on the impact of recent work and thus on current research performance. Results show that the h-index and our bibliometric 'crown indicator' both relate in a quite comparable way with peer judgments. But for smaller groups in fields with 'less heavy citation traffic' the crown indicator appears to be a more appropriate measure of research performance.
