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Modeling the probabilistic distribution of the impact factor


  • Sarabia, José María
  • Prieto, Faustino
  • Trueba, Carmen


The study of the informetric distributions, such as distributions of citations and impact factors is one of the most relevant topics in the current informetric research. Several laws for modeling impact factor based on ranks have been proposed, including Zipf, Lavalette and the two-exponent law proposed by Mansilla et al. (2007). In this paper, the underlying probabilistic quantile function corresponding to the Mansilla's two-exponent law is obtained. This result is particularly relevant, since it allows us to know the underlying population, to learn about all its features and to use statistical inference procedures. Several probabilistic descriptive measures are obtained, including moments, Lorenz and Leimkuhler curves and Gini index. The distribution of the order statistics is derived. Least squares estimates are obtained. The different results are illustrated using the data of the impact factors in eight relevant scientific fields.

Suggested Citation

  • Sarabia, José María & Prieto, Faustino & Trueba, Carmen, 2012. "Modeling the probabilistic distribution of the impact factor," Journal of Informetrics, Elsevier, vol. 6(1), pages 66-79.
  • Handle: RePEc:eee:infome:v:6:y:2012:i:1:p:66-79
    DOI: 10.1016/j.joi.2011.09.005

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    References listed on IDEAS

    1. Sarabia, J. -M. & Castillo, Enrique & Slottje, Daniel J., 1999. "An ordered family of Lorenz curves," Journal of Econometrics, Elsevier, vol. 91(1), pages 43-60, July.
    2. Mansilla, R. & Köppen, E. & Cocho, G. & Miramontes, P., 2007. "On the behavior of journal impact factor rank-order distribution," Journal of Informetrics, Elsevier, vol. 1(2), pages 155-160.
    3. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    4. Mishra, SK, 2010. "A note on empirical sample distribution of journal impact factors in major discipline groups," MPRA Paper 20747, University Library of Munich, Germany.
    5. Sarabia, José María, 2008. "A general definition of the Leimkuhler curve," Journal of Informetrics, Elsevier, vol. 2(2), pages 156-163.
    6. Egghe, L., 2009. "Mathematical derivation of the impact factor distribution," Journal of Informetrics, Elsevier, vol. 3(4), pages 290-295.
    7. Juan Miguel Campanario, 2010. "Distribution of ranks of articles and citations in journals," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 61(2), pages 419-423, February.
    8. Balakrishnan, N. & Sarabia, José María & Kolev, Nikolai, 2010. "A simple relation between the Leimkuhler curve and the mean residual life," Journal of Informetrics, Elsevier, vol. 4(4), pages 602-607.
    9. Waltman, L. & van Eck, N.J.P., 2009. "Some Comments on Egghe’s Derivation of the Impact Factor Distribution," ERIM Report Series Research in Management ERS-2009-016-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    10. Sarabia, José María & Gómez-Déniz, Emilio & Sarabia, María & Prieto, Faustino, 2010. "A general method for generating parametric Lorenz and Leimkuhler curves," Journal of Informetrics, Elsevier, vol. 4(4), pages 524-539.
    11. Waltman, Ludo & van Eck, Nees Jan, 2009. "Some comments on Egghe's derivation of the impact factor distribution," Journal of Informetrics, Elsevier, vol. 3(4), pages 363-366.
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    Cited by:

    1. Cerovšek, Tomo & Mikoš, Matjaž, 2014. "A comparative study of cross-domain research output and citations: Research impact cubes and binary citation frequencies," Journal of Informetrics, Elsevier, vol. 8(1), pages 147-161.
    2. Richard S.J. Tol, 2013. "Measuring catch-up growth in malnourished populations," Working Paper Series 6013, Department of Economics, University of Sussex Business School.
    3. Alina MOROSANU, 2013. "Empirical Study Of Different Factors Effects On Articles Publication Regarding Survey Interviewer Characteristics Using Multilevel Regression Model," Management and Marketing Journal, University of Craiova, Faculty of Economics and Business Administration, vol. 0(1), pages 141-156, May.
    4. Tol, Richard S.J., 2013. "Identifying excellent researchers: A new approach," Journal of Informetrics, Elsevier, vol. 7(4), pages 803-810.
    5. Jiann-wien Hsu & Ding-wei Huang, 2016. "Impact factor distribution revisited with graphical representation," Scientometrics, Springer;Akadémiai Kiadó, vol. 107(3), pages 1321-1329, June.
    6. Brzezinski, Michal, 2014. "Empirical modeling of the impact factor distribution," Journal of Informetrics, Elsevier, vol. 8(2), pages 362-368.


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