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.
Similar content being viewed by others
References
Barcza, K., & Telcs, A. (2009). Paretian publication patterns imply Paretian Hirsch index. Scientometrics, 81(2), 513–519.
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.
David, H. A., & Nagaraja, H. N. (2003). Order statistics (3rd ed.). New Jersey: Wiley.
Egghe, L., & Rousseau, R. (2008). An h-index weighted by citation impact. Information Processing & Management, 44(2), 770–780.
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.
Glänzel, W. (2008a). On some new bibliometric applications of statistics related to the h-index. Scientometrics, 77(1), 187–196.
Glänzel, W. (2008b). What are your best papers? ISSI Newsletter, 4(4), 64–67.
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.
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.
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.
Hill, B. M. (1975). A simple general approach to inference about the tail of a distribution. Annals of Statistics, 3, 1663–1674.
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.
Johnson, N. L., Kotz, S., & Balakrishnan, N. (1994). Continuous univariate distributions (2nd ed., Vol. 1). New York: John Wiley & Sons.
Pao, M. L. (1986). An empirical examination of Lotka’s law. Journal of the American Society for Information Science, 37(1), 26–33.
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.
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/.
Schubert, A., & Glänzel, W. (2007). A systematic analysis of Hirsch-type indices for journals. Journal of Informetrics, 1(3), 179–184.
Schubert, A., Glänzel, W., & Braun, T. (1987). Subject field characteristic citation scores and scales for assessing research performance. Scientometrics, 12(5–6), 267–291.
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.
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.
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.
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
Corresponding author
Rights 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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11192-009-0124-9