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  • Author or Editor: Leo Egghe x
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Abstract  

This article calculates probabilities for the occurrence of different types of papers such as genius papers, basic papers, ordinary papers or insignificant papers. The basis of these calculations are the formulae for the cumulative nth citation distribution, being the cumulative distribution of times at which articles receive their nth(n = 1,2,3,...) citation. These formulae (proved in previous papers) are extended to allow for different aging rates of the papers. These new results are then used to define different importance classes of papers according to the different values of n, in function of time t. Examples are given in case of a classification into four parts: genius papers, basic papers, ordinary papers and (almost) insignificant papers. The fact that, in these examples, the size of each class is inversely related to the importance of the journals in this class is proved in a general mathematical context in which we have an arbitrary number of classes and where the threshold values of n in each class are defined according to the natural law of Weber-Fechner.

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Abstract  

The following problem has never been studied : Given A, the total number of items (e.g. articles) and T, the total number of sources (e.g. journals that contain these articles) (hence A>T), when is there a Lotka function.

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Abstract  

From a list of papers of an author, ranked in decreasing order of the number of citations to these papers one can calculate this author’s Hirsch index (or h-index). If this is done for a group of authors (e.g. from the same institute) then we can again list these authors in decreasing order of their h-indices and from this, one can calculate the h-index of (part of) this institute. One can go even further by listing institutes in a country in decreasing order of their h-indices and calculate again the h-index as described above. Such h-indices are called by Schubert [2007] “successive” h-indices. In this paper we present a model for such successive h-indices based on our existing theory on the distribution of the h-index in Lotkaian informetrics. We show that, each step, involves the multiplication of the exponent of the previous h-index by 1/α where α > 1 is a Lotka exponent. We explain why, in general, successive h-indices are decreasing. We also introduce a global h-index for which tables of individuals (authors, institutes,...) are merged. We calculate successive and global h-indices for the (still active) D. De Solla Price awardees.

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Abstract  

This paper studies four different h-index sequences (different in publication periods and/or citation periods). Lotkaian models for these h-index sequences are presented by mutual comparison of one sequence with another one. We also give graphs of these h-sequences for this author on which a discussion is presented. The same is done for the g-index and the R-index.

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