Distributions of the h-index and the g-index

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 and supposing the scientist-article IPP to be Lotkaian with exponent α, we have that the scientist-h-index IPP and the scientist-g-index IPP are Lotkaian with exponent . 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 αα∗. 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.