The H irsch index of a shifted L otka function and its relation with the impact factor

Leo Egghe · Ronald Rousseau

20 citations0/0 files storedJournal of the American Society for Information Science and Technology

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scientometrics and bibliometrics research Psychology Research and Bibliometrics Web visibility and informetrics

Abstract

Based on earlier results about the shifted Lotka function, we prove an implicit functional relation between the Hirsch index (h‐index) and the total number of sources (T). It is shown that the corresponding function, h(T), is concavely increasing. Next, we construct an implicit relation between the h‐index and the impact factor IF (an average number of items per source). The corresponding function h(IF) is increasing and we show that if the parameter C in the numerator of the shifted Lotka function is high, then the relation between the h‐index and the impact factor is almost linear.

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References

2005An index to quantify an individual's scientific research output 1926The frequency distribution of scientific productivity 2006An informetric model for the Hirsch-index 2005Power Laws in the Information Production Process: Lotkaian Informetrics 2010Evaluating Journal Quality: Is the H-Index a Better Measure Than Impact Factors?2004Article impact calculated over arbitrary periods 2011Thoughts on uncitedness: Nobel laureates and Fields medalists as case studies 2009The role of the h-index and the characteristic scores and scales in testing the tail properties of scientometric distributions

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2012The functional relation between the impact factor and the uncitedness factor revisited 2013Formulae for the h‐index: A lack of robustness in L otkaian informetrics?2012Comparison of different mathematical functions for the analysis of citation distribution of papers of individual authors 2013The individual author’s publication–citation process: theory and practice

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