7 research outputs found
Characterisation of the x-index and the rec-index
Axiomatic characterisation of a bibliometric index provides insight into the properties
that the index satisfies and facilitates the comparison of different indices. A geometric
generalisation of the h-index, called the x-index, has recently been proposed to address
some of the problems with the h-index, in particular, the fact that it is not scale invariant,
i.e., multiplying the number of citations of each publication by a positive constant may
change the relative ranking of two researchers. While the square of the h-index is the area
of the largest square under the citation curve of a researcher, the square of the x-index,
which we call the rec-index (or rectangle-index), is the area of the largest rectangle under
the citation curve. Our main contribution here is to provide a characterisation of the
rec-index via three properties: monotonicity, uniform citation and uniform equivalence.
Monotonicity is a natural property that we would expect any bibliometric index to satisfy,
while the other two properties constrain the value of the rec-index to be the area of the
largest rectangle under the citation curve. The rec-index also allows us to distinguish
between in
uential researchers who have relatively few, but highly-cited, publications
and prolific researchers who have many, but less-cited, publications
Ranking of Indian Corporate Medical Institutions and Their Performance
The performance index (P-index) is an interesting parameter to calculate the individual strength among the teaching hospitals. There is the determination of the Indian corporate Medical Institutions to establish themselves in both academic, patient care and research field. Healthcare, teaching and research are basic components of research activities in healthcare sector. This study highlights the research growth, comparative growth, collaboration of researchers and ranking of the teaching hospitals according to P-index
A new bibliometric index based on the shape of the citation distribution
In order to improve the h-index in terms of its accuracy and sensitivity to the form of the citation distribution, we propose the new bibliometric index . The basic idea is to define, for any author with a given number of citations, an “ideal” citation distribution which represents a benchmark in terms of number of papers and number of citations per publication, and to obtain an index which increases its value when the real citation distribution approaches its ideal form. The method is very general because the ideal distribution can be defined differently according to the main objective of the index. In this paper we propose to define it by a “squared-form” distribution: this is consistent with many popular bibliometric indices, which reach their maximum value when the distribution is basically a “square”. This approach generally rewards the more regular and reliable researchers, and it seems to be especially suitable for dealing with common situations such as applications for academic positions. To show the advantages of the -index some mathematical properties are proved and an application to real data is proposed.Web of Science912art. no. e11596
Ranking authors using fractional counting of citations : an axiomatic approach
This paper analyzes from an axiomatic point of view a recent proposal for counting citations: the value of a citation given by a paper is inversely proportional to the total number of papers it cites. This way of fractionally counting citations was suggested as a possible way to normalize citation counts between fields of research having different citation cultures. It belongs to the “citing-side” approach to normalization. We focus on the properties characterizing this way of counting citations when it comes to ranking authors. Our analysis is conducted within a formal framework that is more complex but also more realistic than the one usually adopted in most axiomatic analyses of this kind
Journal ranking should depend on the level of aggregation
Journal ranking is becoming more important in assessing the quality of
academic research. Several indices have been suggested for this purpose,
typically on the basis of a citation graph between the journals. We follow an
axiomatic approach and find an impossibility theorem: any self-consistent
ranking method, which satisfies a natural monotonicity property, should depend
on the level of aggregation. Our result presents a trade-off between two
axiomatic properties and reveals a dilemma of aggregation.Comment: 10 pages, 2 figure
Nash's bargaining problem and the scale-invariant Hirsch citation index
A number of citation indices have been proposed for measuring and ranking the
research publication records of scholars. Some of the best known indices, such
as those proposed by Hirsch and Woeginger, are designed to reward most highly
those records that strike some balance between productivity (number of papers
published), and impact (frequency with which those papers are cited). A large
number of rarely cited publications will not score well, nor will a very small
number of heavily cited papers. We discuss three new citation indices, one of
which was independently proposed in \cite{FHLB}. Each rests on the notion of
scale invariance, fundamental to John Nash's solution of the two-person
bargaining problem. Our main focus is on one of these -- a scale invariant
version of the Hirsch index. We argue that it has advantages over the original;
it produces fairer rankings within subdisciplines, is more decisive
(discriminates more finely, yielding fewer ties) and more dynamic (growing over
time via more frequent, smaller increments), and exhibits enhanced centrality
and tail balancedness. Simulations suggest that scale invariance improves
robustness under Poisson noise, with increased decisiveness having no cost in
terms of the number of ``accidental" reversals, wherein random irregularities
cause researcher A to receive a lower index value than B, although A's
productivity and impact are both slightly higher than B's. Moreover, we provide
an axiomatic characterization of the scale invariant Hirsch index, via axioms
that bear a close relationship, in discrete analogue, to those used by Nash in
\cite{Nas50}. This argues for the mathematical naturality of the new index.
An earlier version was presented at the 5th World Congress of the Game Theory
Society, Maastricht, Netherlands in 2016.Comment: 44 pages, 8 figure