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H Index: A Statistical Proposal

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  • Paola Cerchiello

    () (Department of Economics and Management, University of Pavia)

  • Paolo Giudici

    (Department of Economics and Management, 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 all 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, typically from an asymptotic viewpoint. In the present work we propose an exact 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 exact confidence intervals to compare authors as well as quality control thresholds that can be used as target values.

Suggested Citation

  • Paola Cerchiello & Paolo Giudici, 2013. "H Index: A Statistical Proposal," DEM Working Papers Series 039, University of Pavia, Department of Economics and Management.
  • Handle: RePEc:pav:demwpp:039
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    File URL: http://economia.unipv.it/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0039.pdf
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    References listed on IDEAS

    as
    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. 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.
    4. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, 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.
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