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

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 article on 206 mathematics journals. This distribution is of a completely different nature than the impact factor (IF) rank-order distribution which (as proved in a previous article) is S-shaped. This is also confirmed by our example. Only in the log–log scale of the h-index distribution do we notice a concave deviation of the straight line for higher ranks. This phenomenon is discussed.