Among the most popular scientific impact indicators is the $h$-index, proposed by J. Hirsch (2005). It has been defined as follows. An author who had published $n$ papers has the Hirsch index equal to $H$, if each of his $H$ publications were cited at least $H$ times, and each of the other $n-H$ items were cited no more than $H$ times. This simple bibliometric indicator quickly received much attention in the academic community and started to be a subject of intensive research. It was noted that contrary to earlier approaches, i.e. publication count, citation count etc., this measure both concerns productivity and impact of an individual.
In a broader perspective, this issue is a special case of the so-called Producer Assessment Problem (Gagolewski, Grzegorzewski, 2010b). Its main aim is to analyze (both theoretically and empirically) a special class of aggregation operators (see Grabisch et al, 2009) called impact functions.
The CITAN package consists of three types of tools. Given a numeric vector, the first class of functions computes the values of certain impact functions. Among them are:
index.h
),index.g
),index.rp
andindex.lp
), which
generalize the$h$-index and the$w$-index (Woeginger, 2008), andSstat
andSstat2
),
which generalize the OWMax operators (Dubois et al, 1988)
and the$h$- and$r_\infty$-indices.Additionally, a set of functions dealing with stochastic aspects of the class of S-statistics and the Pareto type-II family of distributions is included (Gagolewski, Grzegorzewski, 2010a). We have the following. The functions that work for any continuous distribution (see Gagolewski, Grzegorzewski, 2010a):
psstat
,dsstat
for computing the distribution of S-statistics
generated by a control function,phirsch
,dhirsch
for computing the distribution of the Hirsch index,rho.get
for computing the so-called$\kappa$-index ($\rho_\kappa$),
which is a particular location characteristic of a given probability distribution
depending on a control function$\kappa$.ppareto2
,dpareto2
,qpareto2
,rpareto2
for general functions dealing with the Pareto distribution of the second kind,
including the c.d.f., p.d.f, quantiles and random deviates,pareto2.htest
--- two-sample$h$-test for equality of shape parameters based on the difference of$h$-indices,pareto2.htest.approx
--- two-sample asymptotic (approximate)$h$-test,pareto2.ftest
--- two-sample exact F-test for equality of shape parameters,pareto2.zsestimate
--- estimation of parameters using the Bayesian method (MMSE) developed by Zhang and Stevens (2009),pareto2.mlekestimate
--- estimation of shape parameter using the unbiased MLE,pareto2.goftest
--- goodness-of-fit tests,pareto2.confint.rho
andpareto2.confint.rho.approx
--- exact and approximate (asymptotic)
confidence intervals for the$\kappa$-index basing on S-statistics,pareto2.confint.h
--- exact confidence intervals for the theoretical$h$-index.Moreover, we have implemented some simple graphical methods than may be used
to illustrate various aspects of data being analyzed,
see plot.citfun
, curve.add.rp
, and curve.add.lp
.
Please feel free to send any comments and suggestions (e.g.
to include some new bibliometric impact indices) to the author
(see also
For a complete list of functions, use library(help="CITAN")
.
Keywords: Hirsch's h-index, Egghe's g-index, L-statistics, S-statistics, bibliometrics, scientometrics, informetrics, webometrics, aggregation operators, impact functions, impact assessment.