CITAN (version 2011.03-1)

CITAN-package: CITation ANalysis toolpack

Description

CITAN is a library of functions useful in --- but not limited to --- quantitative research in the field of scientometrics. It also contains various methods for dealing with the Pareto-type II distribution.

Arguments

Details

Fair and objective assessment methods of individual scientists had become the focus of scientometricians' attention since the very beginning of their discipline. A quantitative expression of some publication-citation process characteristics is assumed to be a predictor of broadly conceived scientific competence.

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:

  1. Hirsch's$h$-index (Hirsch, 2005; seeindex.h),
  2. Egghe's$g$-index (Egghe, 2006; seeindex.g),
  3. the$r_p$and$l_p$indices (Gagolewski, Grzegorzewski, 2009a, 2009b; seeindex.rpandindex.lp), which generalize the$h$-index and the$w$-index (Woeginger, 2008), and
  4. S-statistics (Gagolewski, Grzegorzewski, 2010a, 2011; seeSstatandSstat2), 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):

  1. psstat,dsstatfor computing the distribution of S-statistics generated by a control function,
  2. phirsch,dhirschfor computing the distribution of the Hirsch index,
  3. rho.getfor computing the so-called$\kappa$-index ($\rho_\kappa$), which is a particular location characteristic of a given probability distribution depending on a control function$\kappa$.
Tools for the Pareto-type II family:
  1. ppareto2,dpareto2,qpareto2,rpareto2for general functions dealing with the Pareto distribution of the second kind, including the c.d.f., p.d.f, quantiles and random deviates,
  2. pareto2.htest--- two-sample$h$-test for equality of shape parameters based on the difference of$h$-indices,
  3. pareto2.htest.approx--- two-sample asymptotic (approximate)$h$-test,
  4. pareto2.ftest--- two-sample exact F-test for equality of shape parameters,
  5. pareto2.zsestimate--- estimation of parameters using the Bayesian method (MMSE) developed by Zhang and Stevens (2009),
  6. pareto2.mlekestimate--- estimation of shape parameter using the unbiased MLE,
  7. pareto2.goftest--- goodness-of-fit tests,
  8. pareto2.confint.rhoandpareto2.confint.rho.approx--- exact and approximate (asymptotic) confidence intervals for the$\kappa$-index basing on S-statistics,
  9. 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 http://www.ibspan.waw.pl/~gagolews).

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.

References

Dubois D., Prade H., Testemale C., Weighted fuzzy pattern matching, Fuzzy Sets and Systems 28, s. 313-331, 1988. Egghe L., Theory and practise of the g-index, Scientometrics 69(1), 131-152, 2006. Gagolewski M., Grzegorzewski P., Possibilistic analysis of arity-monotonic aggregation operators and its relation to bibliometric impact assessment of individuals, International Journal of Approximate Reasoning, doi:10.1016/j.ijar.2011.01.010. Gagolewski M., Grzegorzewski P., A geometric approach to the construction of scientific impact indices, Scientometrics 81(3), 2009a, 617-634. Gagolewski M., Debski M., Nowakiewicz M., Efficient algorithms for computing ''geometric'' scientific impact indices, Research Report of Systems Research Institute, Polish Academy of Sciences RB/1/2009, 2009b. Gagolewski M., Grzegorzewski P., S-statistics and their basic properties, In: Borgelt C. et al (Eds.), Combining Soft Computing and Statistical Methods in Data Analysis, Springer-Verlag, 2010a, 281-288. Grabisch M., Pap E., Marichal J.-L., Mesiar R.. Aggregation functions, Cambridge, 2009. Hirsch J.E., An index to quantify individual's scientific research output, Proceedings of the National Academy of Sciences 102(46), 16569-16572, 2005. Kosmulski M., MAXPROD - A new index for assessment of the scientific output of an individual, and a comparison with the h-index, Cybermetrics 11(1), 2007. Woeginger G.J., An axiomatic characterization of the Hirsch-index, Mathematical Social Sciences 56(2), 224-232, 2008. Zhang J., Stevens M.A., A New and Efficient Estimation Method for the Generalized Pareto Distribution, Technometrics 51(3), 2009, 316-325.