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Abstract

In this article, for any group of authors, we define three different h-indices. First, there is the successive h-index h2 based on the ranked list of authors and their h-indices h1 as defined by Schubert (2007). Next, there is the h-index hP based on the ranked list of authors and their number of publications. Finally, there is the h-index hC based on the ranked list of authors and their number of citations. We present formulae for these three indices in Lotkaian informetrics from which it also follows that h2 < hp < hc. We give a concrete example of a group of 167 authors on the topic optical flow estimation. Besides these three h-indices, we also calculate the two-by-two Spearman rank correlation coefficient and prove that these rankings are significantly related.

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Abstract

Fractional frequency distributions of, for example, authors with a certain (fractional) number of papers are very irregular and, therefore, not easy to model or to explain. This article gives a first attempt to this by assuming two simple Lotka laws (with exponent 2): one for the number of authors with n papers (total count here) and one for the number of papers with n authors, n E N. Based an an earlier made convolution model of Egghe, interpreted and reworked now for discrete scores, we are able to produce theoretical fractional frequency distributions with only one parameter, which are in very close agreement with the practical ones as found in a large dataset produced earlier by Rao. The article also shows that (irregular) fractional frequency distributions are a consequence of Lotka's law, and are not examples of breakdowns of this famous historical law.

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