Skip to main content
Log in

The role of the h-index and the characteristic scores and scales in testing the tail properties of scientometric distributions

  • Published:
Scientometrics Aims and scope Submit manuscript

Abstract

The tail properties of scientometric distributions are studied in the light of the h-index and the characteristic scores and scales. A statistical test for the h-core is presented and illustrated using the example of four selected authors. Finally, the mathematical relationship between the h-index and characteristic scores and scales is analysed. The results give new insights into important properties of rank-frequency and extreme-value statistics derived from scientometric and informetric processes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  • Barcza, K., & Telcs, A. (2009). Paretian publication patterns imply Paretian Hirsch index. Scientometrics, 81(2), 513–519.

    Article  Google Scholar 

  • Beirlant, J., Einmahl, J. H. J. (2007), Asymptotics for the Hirsch index. CentER Discussion Paper #2007-86. Accessible at: http://arno.uvt.nl/show.cgi?fid=65780).

  • Burrell, Q. L. (2007). On the h-index, the size of the Hirsch core and Jin’s A-index. Journal of Informetrics, 1(2), 170–177.

    Article  MathSciNet  Google Scholar 

  • David, H. A., & Nagaraja, H. N. (2003). Order statistics (3rd ed.). New Jersey: Wiley.

    MATH  Google Scholar 

  • Egghe, L., & Rousseau, R. (2008). An h-index weighted by citation impact. Information Processing & Management, 44(2), 770–780.

    Article  Google Scholar 

  • Glänzel, W. (2006). On the h-index—A mathematical approach to a new measure of publication activity and citation impact. Scientometrics, 67(2), 315–321.

    Article  Google Scholar 

  • Glänzel, W. (2008a). On some new bibliometric applications of statistics related to the h-index. Scientometrics, 77(1), 187–196.

    Article  Google Scholar 

  • Glänzel, W. (2008b). What are your best papers? ISSI Newsletter, 4(4), 64–67.

    Google Scholar 

  • Glänzel, W. (2009). The role of the h-index and the characteristic scores and scales in testing the tail properties of scientometric distributions. In: B. Larsen, J. Leta (Eds.), Proceedings of ISSI 2009—The 12th international conference on scientometrics and informetrics. Rio de Janeiro, pp. 120–130.

  • Glänzel, W., & Schubert, A. (1988a). Characteristic scores and scales in assessing citation impact. Journal of Information Science, 14(2), 123–127.

    Article  Google Scholar 

  • Glänzel, W., & Schubert, A. (1988b). Theoretical and empirical studies of the tail of scientometric distributions. In L. Egghe & R. Rousseau (Eds.), Informetrics 87/88 (pp. 75–83). New York: Elsevier Science Publisher.

    Google Scholar 

  • Glänzel, W., Schubert, A., & Telcs, A. (1984). Goodness of fit test for the tail of distributions. In Bolyai colloquium on goodness of fit. Debrecen, Hungary, June 25–28, 1984.

  • Gumbel, E. J. (1958). Statistics of extremes. New York: Columbia University Press.

    MATH  Google Scholar 

  • Hill, B. M. (1975). A simple general approach to inference about the tail of a distribution. Annals of Statistics, 3, 1663–1674.

    Article  Google Scholar 

  • Hirsch, J. E. (2005). An index to quantify an individual’s scientific research output. Proceedings of the National Academy of Sciences of the United States of America, 102(46), 16569–16572. (Also available at: arXiv:physics/0508025, Accessible via http://arxiv.org/abs/physics/0508025).

  • Jin, B. H., Liang, L. M., Rousseau, R., & Egghe, L. (2007). The R- and AR-indices: Complementing the h-index. Chinese Science Bulletin, 52(6), 855–863.

    Article  Google Scholar 

  • Johnson, N. L., Kotz, S., & Balakrishnan, N. (1994). Continuous univariate distributions (2nd ed., Vol. 1). New York: John Wiley & Sons.

    MATH  Google Scholar 

  • Pao, M. L. (1986). An empirical examination of Lotka’s law. Journal of the American Society for Information Science, 37(1), 26–33.

    Google Scholar 

  • Persson, O., Glänzel, W., & Danell, R. (2004). Inflationary bibliometric values: The role of scientific collaboration and the need for relative indicators in evaluative studies. Scientometrics, 60(3), 421–432.

    Article  Google Scholar 

  • Rousseau, R. (2006), New developments related to the Hirsch index. Science Focus, 1(4), 23–25 (in Chinese); English version accessible at http://eprints.rclis.org/archive/00006376/.

    Google Scholar 

  • Schubert, A., & Glänzel, W. (2007). A systematic analysis of Hirsch-type indices for journals. Journal of Informetrics, 1(3), 179–184.

    Article  Google Scholar 

  • Schubert, A., Glänzel, W., & Braun, T. (1987). Subject field characteristic citation scores and scales for assessing research performance. Scientometrics, 12(5–6), 267–291.

    Article  Google Scholar 

  • Schubert, A., Glänzel, W., & Braun, T. (1989). Scientometric datafiles. A comprehensive set of indicators on 2649 journals and 96 countries in all major fields and subfields 1981–1985. Scientometrics, 16(1–6), 3–478.

    Article  Google Scholar 

  • Schubert, A., & Telcs, A. (1989). Estimation of the publication potential in 50 U.S. states and in the District of Columbia based on the frequency distribution of scientific productivity. Journal of the American Society for Information Science, 40(4), 291–297.

    Article  Google Scholar 

  • Zitt, M., Bassecoulard, E., Filliatreau, G., & Ramanana-Rahary, S. (2007). Revisiting country and institution indicators from citation distributions: Profile performance measures. Proceedings of ISSI 2007: 11th international conference of the international society for scientometrics and informetrics, pp. 797–802.

Download references

Acknowledgement

An extended version of a paper presented at the 12th International Conference on Scientometrics and Informetrics, Rio de Janeiro (Brazil), 14–17 July 2009 (Glänzel 2009).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wolfgang Glänzel.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glänzel, W. The role of the h-index and the characteristic scores and scales in testing the tail properties of scientometric distributions. Scientometrics 83, 697–709 (2010). https://doi.org/10.1007/s11192-009-0124-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11192-009-0124-9

Keywords

Navigation