, Volume 121, Issue 3, pp 1707–1715 | Cite as

Measures of linear type lead to a characterization of Zipf functions

  • Leo Egghe
  • Ronald RousseauEmail author


In this contribution we introduce the notion of a measure (or indicator) of linear type. Combining ideas related to power functions, in particular Zipf’s function, and h-type indices, we come to a novel characterization of general power functions and Zipf’s functions.


Zipf’s law h-index g-index Measures of linear type 



We thank anonymous reviewers for correcting some typos in the mathematical formulae and for useful remarks, leading to the ‘discussion’ section.


  1. Auerbach, F. (1913). Das Gesetz der Bevölkerungskonzentration. Petermanns Mitteilungen,59(1), 74–76.Google Scholar
  2. Axtell, R. L. (2001). Zipf distribution of US firm sizes. Science,293(5536), 1818–1820.CrossRefGoogle Scholar
  3. Bouyssou, D., & Marchant, T. (2011). Ranking scientists and departments in a consistent manner. Journal of the American Society for Information Science and Technology,62(9), 1761–1769.CrossRefGoogle Scholar
  4. Condon, E. V. (1928). Statistics of vocabulary. Science,67(1733), 300.CrossRefGoogle Scholar
  5. Egghe, L. (2005). Power laws in the information production process: Lotkaian informetrics. Amsterdam: Elsevier.CrossRefGoogle Scholar
  6. Egghe, L. (2006a). An improvement of the h-index: The g-index. ISSI Newsletter,2(1), 8–9.MathSciNetGoogle Scholar
  7. Egghe, L. (2006b). Theory and practise of the g-index. Scientometrics,69(1), 131–152.MathSciNetCrossRefGoogle Scholar
  8. Egghe, L., & Rousseau, R. (2019). Solution by step functions of a minimum problem in L2[0, T], using generalized h- and g-indices. Journal of Informetrics,13(3), 785–792.CrossRefGoogle Scholar
  9. Estoup, J. B. (1916). Gammes Sténographiques: Méthode et exercices pour l’acquisition de la vitesse (4th ed.). Paris: Institut Sténographique de France.Google Scholar
  10. Ferrer-i-Cancho, R., & Sole, R. V. (2003). Least effort and the origins of scaling in human language. Proceedings of the National Academy of Sciences of the United States of America,100(3), 788–791.MathSciNetCrossRefGoogle Scholar
  11. Furusawa, C., & Kaneko, K. (2003). Zipf’s law in gene expression. Physical Review Letters,90(8), 88102.CrossRefGoogle Scholar
  12. 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.CrossRefGoogle Scholar
  13. Lotka, A. J. (1926). The frequency distribution of scientific productivity. Journal of the Washington Academy of Sciences,16(12), 317–323.Google Scholar
  14. Newman, M. E. J. (2005). Power laws, Pareto distributions and Zipf’s law. Contemporary Physics,46(5), 323–351.CrossRefGoogle Scholar
  15. Qomi, M. J. A., Noshadravan, A., Sobstyl, J. M., Toole, J., Ferreira, J., Pellenq, R. J.-M., et al. (2016). Data analytics for simplifying thermal efficiency planning in cities. Journal of the Royal Society, Interface,13(117), 20150971.CrossRefGoogle Scholar
  16. Rousseau, R. (2016). Citation data as proxy for quality or scientific influence are at best PAC (Probably Approximately Correct). Journal of the Association for Information Science and Technology,67(12), 3092–3094.CrossRefGoogle Scholar
  17. Salvati, P., Bianchi, C., Rossi, M., & Guzzetti, F. (2010). Societal landslide and flood risk in Italy. Natural Hazards and Earth System Sciences,10(3), 465–483.CrossRefGoogle Scholar
  18. Tria, F., Loreto, V., Servedio, V. D. P., & Strogatz, S. H. (2014). The dynamics of correlated novelties. Scientific Reports,4, 5890.CrossRefGoogle Scholar
  19. van Eck, N. J., & Waltman, L. (2008). Generalizing the h-and g-indices. Journal of Informetrics,2(4), 263–271.CrossRefGoogle Scholar
  20. Waltman, L., & van Eck, N.-J. (2012). The inconsistency of the h-index. Journal of the American Society for Information Science and Technology,63(2), 406–415.CrossRefGoogle Scholar
  21. Zipf, G.K. (1935). The psycho-biology of language: An introduction to dynamic philology. Houghton Mifflin. Reprinted: (1968). Cambridge, Mass.: The M.I.T. Press.Google Scholar
  22. Zipf, G.K. (1949). Human behavior and the principle of least effort. Cambridge (Mass.): Addison-Wesley Press.Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.University of HasseltHasseltBelgium
  2. 2.Faculty of Social SciencesUniversity of AntwerpAntwerpBelgium
  3. 3.Centre for R&D Monitoring (ECOOM) and Department of MSIKU LeuvenLeuvenBelgium

Personalised recommendations