A new bibliometric index based on the shape of the citation distribution

In order to improve the h-index in terms of its accuracy and sensitivity to the form of the citation distribution, we propose the new bibliometric index [symbol in text]. The basic idea is to define, for any author with a given number of citations, an "ideal" citation distribution which represents a benchmark in terms of number of papers and number of citations per publication, and to obtain an index which increases its value when the real citation distribution approaches its ideal form. The method is very general because the ideal distribution can be defined differently according to the main objective of the index. In this paper we propose to define it by a "squared-form" distribution: this is consistent with many popular bibliometric indices, which reach their maximum value when the distribution is basically a "square". This approach generally rewards the more regular and reliable researchers, and it seems to be especially suitable for dealing with common situations such as applications for academic positions. To show the advantages of the [symbol in text]-index some mathematical properties are proved and an application to real data is proposed.