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Abstract

In one of the first attempts at providing a mathematical framework for the Hirsch index, Egghe and Rousseau (2006) assumed the standard Lotka model for an author's citation distribution to derive a delightfully simple closed formula for his/her h-index. More recently, the same authors (Egghe & Rousseau, 2012b) have presented a new (implicit) formula based on the so-called shifted Lotka function to allow for the objection that the original model makes no allowance for papers receiving zero citations. Here it is shown, through a small empirical study, that the formulae actually give very similar results whether or not the uncited papers are included. However, and more important, it is found that they both seriously underestimate the true h-index, and we suggest that the reason for this is that this is a context-the citation distribution of an author-in which straightforward Lotkaian informetrics is inappropriate. Indeed, the analysis suggests that even if we restrict attention to the upper tail of the citation distribution, a simple Lotka/Pareto-like model can give misleading results.

Object

h-index

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Abstract

In this article we further develop the theory for a stochastic model for the citation process in the presence of obsolescence to predict the future citation pattern of individual papers in a collection. More precisely, we investigate the conditional distribution-and its mean- of the number of citations to a paper after time t, given the number of citations it has received up to time t. In an important parametric case it is shown that the expected number of future citations is a linear function of the current number, this being interpretable as an example of a success-breeds-success phenomenon.

Date

29. 3.2003 19:22:48

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Abstract

Citation rates are becoming increasingly important in judging the research quality of journals, institutions and departments, and individual faculty. This paper looks at the pattern of citations across different management science journals and over time. A stochastic model is proposed which views the generating mechanism of citations as a gamma mixture of Poisson processes generating overall a negative binomial distribution. This is tested empirically with a large sample of papers published in 1990 from six management science journals and found to fit well. The model is extended to include obsolescence, i.e., that the citation rate for a paper varies over its cited lifetime. This leads to the additional citations distribution which shows that future citations are a linear function of past citations with a time-dependent and decreasing slope. This is also verified empirically in a way that allows different obsolescence functions to be fitted to the data. Conclusions concerning the predictability of future citations, and future research in this area are discussed.

Date

26.12.2007 19:22:05

Theme

Citation indexing

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Abstract

A recently proposed stochastic model to describe the citation process in the presence of obsolescence is used to answer the question: If a paper has not been cited by time t after its publication, what is the probability that it will ever be cited?

Theme

Citation indexing

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Abstract

In a recent article, L. Egghe, R. Guns, and R. Rousseau () noted that in a study of some eminent scientists, many of them had a fair proportion of papers which were uncited and found this to be surprising. Here, we use the stochastic publication/citation model of Q.L. Burrell () to show that the result might in fact be expected. This brief communication is in the spirit of Q.L. Burrell (, ), showing that results that might at first sight seem to be surprising can in fact often be explainable in a stochastic framework.

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Object

h-index