Hirsch-type characteristics of the tail of distributions. The generalised h-index

In this paper a generalisation of the h-index and g-index is given on the basis of non-negative real-valued functionals defined on subspaces of the vector space generated by the ordered samples. Several Hirsch-type measures are defined and their basic properties are analysed. Empirical properties are illustrated using examples from the micro- and meso-level. Among these measures, the h-index proved the most, the arithmetic and geometric g-indices, the least robust measures. The μ-index and the harmonic g-index provide more balanced results and are still robust enough.