IDEAS home Printed from
   My bibliography  Save this paper

H Index: A Statistical Proposal


  • Paola Cerchiello

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

  • Paolo Giudici

    (Department of Economics and Management, University of Pavia)


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

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pav:demwpp:039. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Alice Albonico). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.