A Critique of Hirsch's Citation Index: A Combinatorial Fermi Problem

@article{Yong2014ACO,
  title={A Critique of Hirsch's Citation Index: A Combinatorial Fermi Problem},
  author={Alexander Yong},
  journal={Notices of the American Mathematical Society},
  year={2014},
  volume={61},
  pages={1040-1051}
}
  • A. Yong
  • Published 18 February 2014
  • Physics
  • Notices of the American Mathematical Society
1.1. Overview. In 2005, physicist J. E. Hirsch [Hi05] proposed theh-index to measure the quality of a researcher’s output. This metric is the largest integer n such that the person has n papers with at least n citations each, and all other papers have weakly less than n citations. Although the original focus of loc. cit. was on physicists, the h-index is now widely popular. For example, Google Scholar and the Web of Science highlight theh-index, among other metrics such as total citation count… 

Figures and Tables from this paper

Summer projects 2014 – 2015 Hirsch ’ s Citation Index and Limit Shape of Random Partitions
Hirsch [3] introduced his h-index to measure the quality of a researcher’s output, defined as the largest integer n such that the person has n papers with at least n citations each. The h-index has
Noncumulative measures of researcher citation impact
TLDR
This work single out six measures from the rather sparse literature, including Hirsch’s m-index, a time-scaled version of the h- index, and introduces new measures based on the idea of “citation acceleration,” which shows substantial promise for future use.
A Bayesian h‐index: How to measure research impact
TLDR
This paper proposes a negative binomial distribution to jointly model the two main components of the h index: the number of papers and their citations and proposes a Bayesian model that allows to obtain posterior inferences on the parameters of the distribution and, in addition, a predictive distribution for the hindex itself.
A Quick Empirical Reproof of the Asymptotic Normality of the Hirsch Citation Index (First proved by Canfield, Corteel, and Savage)
Once upon a time there was an esoteric and specialized notion, called "size of the Durfee square", of interest to at most 100 specialists in the whole world. Then it was kissed by a prince called
Detecting potential reference list manipulation within a citation network
TLDR
Examining a subset of active, highly published authors in PubMed, the frequency of non-self citations to one author coming from one paper approximates Zipf’s law and the Gini Index is proposed as a simple means of quantifying skew in this distribution and tested against a series of “red flag” metrics that are expected to result from RLM attempts.
A simple model for citation curve
TLDR
A simple equation is presented that can be used to derive closed-form expressions for various citation indices, analyze the effect of time and identify individual contribution to the Hirsch index for a group.
fCite: a fractional citation tool to quantify an individual’s scientific research output
TLDR
The fCite web service is presented, a tool for the in-depth analysis of an individual's scientific research output by considering multiple metrics to provide greater insight into a scientist’s multifaceted profile.
Fair ranking of researchers and research teams
TLDR
While the full counting scheme often leads to completely incorrect and misleading ranking, the fractional or authorship-weighted schemes are more accurate and applicable to ranking of researchers as well as research teams and suppress differences in ranking among scientific disciplines.
...
...

References

SHOWING 1-10 OF 13 REFERENCES
Beyond the Durfee square: Enhancing the h-index to score total publication output
TLDR
It is argued that the hT-index is superior to h, both theoretically (it scores all citations), and because it shows smooth increases from year to year as compared with the irregular jumps seen in h.
The Joseph Greenberg Problem: Combinatorics and Comparative Linguistics
We correct a 1957 combinatorial enumeration by the linguist J. Greenberg. The desired count, the Bell number B(25), supported using his Mass Comparison method for language classification. In 1987, he
Analytic Combinatorics
TLDR
This text can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study, and is certain to become the definitive reference on the topic.
Asymptotic analysis of random partitions ∗
In this paper we aim to review some works on the asymptotic behaviors of random partitions. The focus is upon two basic probability models— uniform partitions and Plancherel partitions. One of
Introductory Combinatorics
TLDR
A long-overdue new edition of a popular set, Introductory Combinatorics, Third Edition, presents a broad comprehensive survey of modern combinatorics that is important to the various scientific fields of study.
Scaling the h-index for different scientific ISI fields
We propose a simple way to put in a common scale the h values of researchers working in different scientific ISI fields, so that the foreseeable misuse of this index for inter-areas comparison might
Pecharromán, Scaling the h-index for different scientific ISI fields, Scientometrics
  • Issue
  • 2007
Elect. J. Comb
  • Elect. J. Comb
  • 1998
Making Estimates in Research and Elsewhere , http://physics.illinois.edu/undergrad/ SeniorThesis/EstimatesResearch.pdf [FlSe09] P. Flajolet and R. Sedgewick, Analytic Combinatorics
  • Making Estimates in Research and Elsewhere , http://physics.illinois.edu/undergrad/ SeniorThesis/EstimatesResearch.pdf [FlSe09] P. Flajolet and R. Sedgewick, Analytic Combinatorics
  • 2009
...
...