A refinement of Egghe's increment studies: an alternative version

Rousseau, Ronald A refinement of Egghe's increment studies: an alternative version., 2013 [Preprint]

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English abstract

In this contribution we show how results obtained in a series of papers by Egghe can be refined in the sense that we need fewer conditions. In these articles Egghe considered a general h-type index which has a value n if n is the largest natural number such that the first n publications (ranked according to the number of received citations) have received at least f(n) citations, with f(n) any increasing function defined on the strictly positive numbers. His results deal with increments I2 and I1 defined by: I2(n)= I1(n+1)-I1n) where I1(n)=(n+1)f(n+1)-nf(n). Our results differ from Egghe’s because we also consider I0(n) = nf(n). This version differs from the original one (Rousseau, 2014) by the fact that we (try to) use standard methods for solving difference equations. These methods are recalled in an appendix.

Item type: Preprint
Keywords: characterizations of informetric indicators; increments; forward differences; difference equations
Subjects: B. Information use and sociology of information > BB. Bibliometric methods
Depositing user: Ronald Rousseau
Date deposited: 25 Nov 2013 09:19
Last modified: 02 Oct 2014 12:29
URI: http://hdl.handle.net/10760/20723

References

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Egghe, L. (2013a). A mathematical characterization of the Hirsch-index by means of minimal increments. Journal of Informetrics, 5(3), 439-445.

Egghe, L. (2013b). Mathematical characterizations of the Wu- and Hirsch- indices using two types of minimal increments. Proceedings of ISSI 2013 (J. Gorraiz, E. Schiebel, C. Gumpenberger, M. Hörlesberger, H. Moed, Eds.), pp. 1159-1169. Vienna, Austrian Institute of Technology.

Egghe, L. (2014). A general theory of minimal increments for Hirsch-type indices and applications to the mathematical characterization of Kosmulski-indices (to appear).

Hirsch, J.E. (2005). An index to quantify an individual’s scientific research output. Proceedings of the National Academy of Sciences of the USA, 102(46), 16569-16572.

Hosking, R.J., Joe, S., Joyce, D.C., Turner, J.C. (1996). First steps in numerical analysis (2nd edition). London: Arnold.

Oppenheim, A.V., Willsky, A.S., Young, I.T. (1983). Signals and systems. London: Prentice-Hall.

Rousseau, R. (1997). Numerical Mathematics. Course notes KHBO (in Dutch).

Rousseau, R. (2014). A refinement of Egghe’s increment studies. Journal of Informetrics, 8(1), to appear.

Wu, Q. (2010). The w-index: A measure to assess scientific impact by focusing on widely cited papers. Journal of the American Society for Information Science and Technology, 61(3), 609-614.


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