Completing $h$
Abstract
Nearly a decade ago, the science community was introduced to the -index, a proposed statistical measure of the collective impact of the publications of any individual researcher. It is of course undeniable that any method of reducing a complex data set to a single number will necessarily have certain limitations and introduce certain biases. However, in this paper we point out that the definition of the -index actually suffers from something far deeper: a hidden mathematical incompleteness intrinsic to its definition. In particular, we point out that one critical step within the definition of has been missed until now, resulting in an index which only achieves its stated objectives under certain rather limited circumstances. For example, this incompleteness explains why the -index ultimately has more utility in certain scientific subfields than others. In this paper, we expose the origin of this incompleteness and then also propose a method of completing the definition of in a way which remains close to its original guiding principle. As a result, this "completed" not only reduces to the usual in cases where the -index already achieves its objectives, but also extends the validity of the -index into situations where it currently does not.
Cite
@article{arxiv.1404.2603,
title = {Completing $h$},
author = {Keith R. Dienes},
journal= {arXiv preprint arXiv:1404.2603},
year = {2015}
}
Comments
13 pages, LaTeX, 2 figures, 1 table