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On a statistical h index

Author

Listed:
  • Paola Cerchiello

    (University of Pavia)

  • Paolo Giudici

    (University of Pavia)

Abstract

The measurement of the quality of academic research is a rather controversial issue. Recently Hirsch has proposed a measure that has the advantage of summarizing in a single summary statistics the information that is contained in the citation counts of each scientist. From that seminal paper, a huge amount of research has been lavished, focusing on one hand on the development of correction factors to the h index and on the other hand, on the pros and cons of such measure proposing several possible alternatives. Although the h index has received a great deal of interest since its very beginning, only few papers have analyzed its statistical properties and implications. In the present work we propose a statistical approach to derive the distribution of the h index. To achieve this objective we work directly on the two basic components of the h index: the number of produced papers and the related citation counts vector, by introducing convolution models. Our proposal is applied to a database of homogeneous scientists made up of 131 full professors of statistics employed in Italian universities. The results show that while “sufficient” authors are reasonably well detected by a crude bibliometric approach, outstanding ones are underestimated, motivating the development of a statistical based h index. Our proposal offers such development and in particular confidence intervals to compare authors as well as quality control thresholds that can be used as target values.

Suggested Citation

  • Paola Cerchiello & Paolo Giudici, 2014. "On a statistical h index," Scientometrics, Springer;Akadémiai Kiadó, vol. 99(2), pages 299-312, May.
    • Handle: RePEc:spr:scient:v:99:y:2014:i:2:d:10.1007_s11192-013-1194-2
    DOI: 10.1007/s11192-013-1194-2
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    References listed on IDEAS

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    1. Cerchiello, Paola & Giudici, Paolo, 2012. "On the distribution of functionals of discrete ordinal variables," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2044-2049.
    2. Dalla Valle, L. & Giudici, P., 2008. "A Bayesian approach to estimate the marginal loss distributions in operational risk management," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3107-3127, February.
    3. Roberto Todeschini, 2011. "The j-index: a new bibliometric index and multivariate comparisons between other common indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 87(3), pages 621-639, June.
    4. Wolfgang Glänzel, 2006. "On the h-index - A mathematical approach to a new measure of publication activity and citation impact," Scientometrics, Springer;Akadémiai Kiadó, vol. 67(2), pages 315-321, May.
    5. Izsak, F., 2006. "Maximum likelihood estimation for constrained parameters of multinomial distributions--Application to Zipf-Mandelbrot models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1575-1583, December.
    6. Jan Beirlant & John H. J. Einmahl, 2010. "Asymptotics for the Hirsch Index," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 355-364, September.
    7. Philip Ball, 2005. "Index aims for fair ranking of scientists," Nature, Nature, vol. 436(7053), pages 900-900, August.
    8. Juan E. Iglesias & Carlos Pecharromán, 2007. "Scaling the h-index for different scientific ISI fields," Scientometrics, Springer;Akadémiai Kiadó, vol. 73(3), pages 303-320, December.
    9. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    10. Luca Pratelli & Alberto Baccini & Lucio Barabesi & Marzia Marcheselli, 2012. "Statistical Analysis of the Hirsch Index," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 681-694, December.
    11. Burrell, Quentin L., 2007. "Hirsch's h-index: A stochastic model," Journal of Informetrics, Elsevier, vol. 1(1), pages 16-25.
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    Cited by:

    1. Mutz, Rüdiger & Daniel, Hans-Dieter, 2018. "The bibliometric quotient (BQ), or how to measure a researcher’s performance capacity: A Bayesian Poisson Rasch model," Journal of Informetrics, Elsevier, vol. 12(4), pages 1282-1295.

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