Skip to main content
Log in

Theory and practice of the shifted Lotka function

  • Published:
Scientometrics Aims and scope Submit manuscript

Abstract

One of the major drawbacks of the classical Lotka function is that arguments only start from the value 1. However, in many applications one may want to start from the value 0, e.g. when including zero received citations. In this article we consider the shifted Lotka function, which includes the case of zero items. Basic results for the total number of sources, the total number of items and the average number of items per source are given in this framework. Next we give the rank-frequency function (Zipf-type function) corresponding to the shifted Lotka function and prove their exact relation. The article ends with a practical example which can be fitted by a shifted Lotka function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Ajiferuke, I., & Wolfram, D. (2004). Modelling the characteristics of web page outlinks. Scientometrics, 59(1), 43–62.

    Article  Google Scholar 

  • Burrell, Q. L. (2002). Will this paper ever be cited? Journal of the American Society for Information Science and Technology, 53(3), 232–235.

    Article  Google Scholar 

  • Burrell, Q. L. (2008). Extending Lotkaian informetrics. Information Processing and Management, 44(5), 1794–1807.

    Article  Google Scholar 

  • Egghe, L. (2005). Power laws in the information production process: Lotkaian informetrics. Oxford: Elsevier.

    Google Scholar 

  • Egghe, L., Guns, R., & Rousseau, R. (2011). Thoughts on uncitedness: Nobel laureates and fields medalists as case studies. Journal of the American Society for Information Science and Technology, 62(8), 1637–1644.

    Article  Google Scholar 

  • Egghe, L., & Rousseau, R. (2006). An informetric model for the Hirsch-index. Scientometrics, 69(1), 121–129.

    Article  Google Scholar 

  • Lotka, A. J. (1926). The frequency distribution of scientific productivity. Journal of the Washington Academy of Sciences, 16(12), 317–324.

    Google Scholar 

  • Milojević, S. (2010). Power-law distributions in information science—Making the case for logarithmic binning. Journal of the American Society for Information Science and Technology, 61(12), 2417–2425.

    Article  Google Scholar 

  • Nicholls, P. T. (1987). Estimation of Zipf parameters. Journal of the American Society for Information Science, 38, 443–445. Erratum: Journal of the American Society for Information Science, 39, p. 287 (1988).

    Google Scholar 

  • Pao, M. L. (1985). Lotka’s law: A testing procedure. Information Processing and Management, 21, 305–320.

    Article  Google Scholar 

  • Rousseau, R. (1997). Sitations: An exploratory study. Cybermetrics, 1(1), paper 1. http://www.cindoc.csic.es/cybermetrics/articles/v1i1p1.html.

  • Rousseau, B. & Rousseau, R. (2000). LOTKA: A program to fit a power law distribution to observed frequency data. Cybermetrics, 4(1), paper 4. http://www.cindoc.csic.es/cybermetrics/articles/v4i1p4.html.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ronald Rousseau.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Egghe, L., Rousseau, R. Theory and practice of the shifted Lotka function. Scientometrics 91, 295–301 (2012). https://doi.org/10.1007/s11192-011-0539-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11192-011-0539-y

Keywords

Navigation