Abstract
A model of scientific citation distribution is given. We apply it to understand the role of the Hirsch index as an indicator of scientific publication importance in Mathematics and some related fields. The proposed model is based on a generalization of such well-known distributions as geometric and Sibuya laws. Real data analysis of the Hirsch index and corresponding citation numbers is given.
Highlights
A rather large number of indexes are proposed, which supposedly measure the significance of the scientific publications of an author
The Hirsch Index h is the number of articles that have been cited at least h times each
We dwell on the description of both the positive and negative sides of the Hirsch index after constructing citation models for scientific articles
Summary
A rather large number of indexes are proposed, which supposedly measure the significance of the scientific publications of an author. (i2) Hirsch index of the author [4] (see [5]). It is these two indexes that we consider in the proposed work. Recall the definition of the Hirsch index (see [4]). The Hirsch Index h is the number of articles that have been cited at least h times each. This index was introduced in [4], where its properties were explained. We dwell on the description of both the positive and negative sides of the Hirsch index after constructing citation models for scientific articles. One of them has already been stated by us in preprint [6]
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