The characteristic scores and scales (CSS), introduced by Glänzel and Schubert (J Inform Sci 14:123–127, <cite>1988</cite>) and further studied in subsequent papers of Glänzel, can be calculated exactly in a Lotkaian framework. We prove that these
CSS are simple exponents of the average number of items per source in general IPPs. The proofs are given using size-frequency
functions as well as using rank-frequency functions. We note that CSS do not necessarily have to be defined as averages but
that medians can be used as well. Also for these CSS we present exact formulae in the Lotkaian framework and both types of
CSS are compared. We also link these formulae with the h-index.
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.
Authors:Pedro Albarrán, Juan A. Crespo, Ignacio Ortuño, and Javier Ruiz-Castillo
this same period. These authors work at a low aggregation level, consisting of the 114 sub-fields distinguished at the time in the Journal Citation Reports. They study the shape of citation distributions by applying the CharacteristicScoresandScales
national publication strategy. Share of highly cited papers. The citation impact of each individual paper is compared with the sevenfold of its corresponding subject standard. This threshold is obtained from the method of characteristicscoreandscales
Egghe , L . Characteristicscoresandscales based on h -type indices . Journal of Informetrics 2010 4 1 14 – 22 10.1016/j.joi.2009.06.001 .
Franceschini , F , Maisano , D . The Hirsch spectrum