Power-law distribution of individual Hirsch indices, the comparison of merits in different fields, and the relation to a Pareto distribution

Abstract

A data set of Hirsch indices, $h$, for Finnish scientists in certain fields is statistically analyzed and fitted to $h(n) =Pn^p$ for the $n$-th most-quoted scientist. The precoefficient $P$ is characteristic for the field and the exponent $p$ is about -0.2 for all data sets considered. For Physics, Chemistry and Chemical Engineering, the $P$ are 49.7(8), 41.3(6), and 21.4(6), respectively. These $p$ values correspond to Pareto exponents of about -7 for the distribution of Hirsch indices $h$.