In this paper some new fields of application of Hirsch-related statistics are presented. Furthermore, so far unrevealed properties
of the h-index are analysed in the context of rank-frequency and extreme-value statistics.
The tail properties of scientometric distributions are studied in the light of the h-index and the characteristic scores and
scales. A statistical test for the h-core is presented and illustrated using the example of four selected authors. Finally,
the mathematical relationship between the h-index and characteristic scores and scales is analysed. The results give new insights
into important properties of rank-frequency and extreme-value statistics derived from scientometric and informetric processes.
In recent studies the issue of the relatedness between journal impact factors and other measures of journal impact have been
raised and discussed from both merely empirical and theoretical perspectives. Models of the underlying citation processes
suggest distributions with two or more free parameters. Proceeding from the relation between the journals’ mean citation rate
and uncitedness and the assumption of an underlying Generalised Waring Distribution (GWD) model, it is found that the journal
impact factor alone does not sufficiently describe a journal’s citation impact, while a two-parameter solution appropriately
reflects its main characteristics. For the analysis of highly cited publications an additional model derived from the same
GWD is suggested. This approach results in robust, comprehensible and interpretable solutions that can readily be applied
in evaluative bibliometrics.
The notion of core documents and their application is discussed in the context of scientometric networks. An interesting solution of the problem of the arbitrariness of thresholds emerges from the application of Hirsch-type indices to dense networks as are typically observed in local clustering. Examples from several disciplines in the sciences and social sciences illustrate how these core vertices can be determined using this approach, and visualise how core documents are applied to represent the internal structure of the complete network or of parts of it.