A rationale for the Hirsch-index rank-order distribution and a comparison with the impact factor rank-order distribution

Abstract

We present a rationale for the Hirsch-index rank-order distribution and prove that it is a power law (hence a straight line in the log-log scale). This is confirmed by experimental data of Pyykkö and by data produced in this paper on 206 mathematics journals. This distribution is of a completely different nature than the impact factor (IF) rank-order distribution which (as was proved in a previous paper) is S-shaped. This is also confirmed by our example. Only in the log-log scale of the h-index distribution we notice a concave deviation of the straight line for higher ranks. This phenomenon is discussed.