Egghe, L, Distributions of the h-index and the g-index, PROCEEDINGS OF ISSI 2007: 11TH INTERNATIONAL CONFERENCE OF THE ISSI, VOLS I AND II. 2007. p.245-253

[Eugene Garfield]

Email: leo.egghe at uhasselt.be

Author(s): Egghe, L (Egghe, Leo) 

Title: Distributions of the h-index and the g-index 

Editor(s): TorresSalinas, D; Moed, HF 

Source: PROCEEDINGS OF ISSI 2007: 11TH INTERNATIONAL CONFERENCE OF THE 
INTERNATIONAL SOCIETY FOR SCIENTOMETRICS AND INFORMETRICS, VOLS I AND II 
245-253, 2007 

Cited Reference Count: 18 

Language: English 
Document Type: Article 

Conference Title: 11th International Conference of the International-
Society-for-Scientrometrics-and-Informetrics 

Conference Date: JUN 25-27, 2007 

Conference Location: Madrid, SPAIN 

Conference Sponsors: Int Soc Scientrometr & Informetr, CSIC, Minist Educ & 
Ciencia, FECYT, Comunidad Madrid, Eugene Garfield Fdn, Thomson Sci, 
Elsevier, Journal Informetr, Scopus, Ayuntamiento Madrid, Sci Metrix, Univ 
Carlos III Madrid 

Author Keywords: h-index; hirsch index; g-index; distribution; lotka 

KeyWords Plus: HIRSCH-INDEX; SCIENTISTS; RANKING 

Abstract: In every scientific research area, each scientist has a unique h-
index and g-index. This paper addresses the problem of determining the 
distribution of these indexes over the scientists. We apply aspects of 
linear three-dimensional Lotkaian informetrics to determine these 
distributions. We show that, supposing the article-citation information 
production process (IPP) to be Lotkaian with exponent a and supposing the 
scientist-article IPP to be Lotkaian with exponent alpha*, we have that 
the scientist-h-index IPP and the scientist-g-index IPP are Lotkaian with 
exponent alpha alpha*. This model is proved for discrete as well as 
continuous variables. This shows that the size-frequency distributions of 
the h-index and the g-index are very skew in general due to the generally 
high value of alpha alpha*. We also calculate the rank-frequency 
distributions of the h- and g-index, based on the size-frequency 
distributions in the continuous variables case. Examples are given. 

Addresses: Univ Hasselt, Diepenbeek, B-3590 Belgium. 

Publisher Name: INT SOC SCIENTOMETRICS & INFORMETRICS-ISSI 
Publisher Address: KATHOLIEKE UNIV LEUVEN, FACULTEIT E T E W, DEKENSTRAAT 
2, LEUVEN, B-3000, BELGIUM 

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