In a recent paper1Burrell shows that libraries with lower average borrowings tend to require a larger proportion of their collections to account for 80% of the borrowings, than those with higher average borrowings. In that study, the underlying frequency distribution was a negative binomial. We are dealing with a case when the underlying distribution is of Lotka type. It is also shown that the 80/20-effect is much stronger in this case.
In this short communication we give critical comments on the paper of Perakakis et al. (Scientometrics 85(2):553–559, ) on “Natural selection of academic papers”. The criticism mainly focusses on their unbalanced criticism of peer review and their negative evaluation of the link of peer review with commercial publishing.
In this paper we discuss the possible gaps between several subdisciplines in informetrics and between informetrics and other-metrics disciplines such as econometrics, sociometrics and so on. It is argued that in all these disciplines, common models exist which describe the main points of interest. We also show that many concrete problems in these disciplines can be formulated in the same way and hence have similar solutions. We can conclude with the statement that the possible gaps between these disciplines are smaller than what many researchers in these different areas may feel and hence that many research projects could be set up in a wider framework.
In many papers, the influence of growth on obsolescence is studied but a formal model for such an influence has not been constructed. In this paper, we develop such a model and find different results for the synchronous and for the diachronous study. We prove that, in the synchronous case, an increase of growth implies an increase of the obsolescence, while, in the diachronous case, exactly the opposite mechanism is found. Exact proofs are given, based on the exponential models for growth as well as obsolescence. We leave open a more general theory.
The uncitedness factor of a journal is its fraction of uncited articles. Given a set of journals (e.g. in a field) we can
determine the rank-order distribution of these uncitedness factors. Hereby we use the Central Limit Theorem which is valid
for uncitedness factors since it are fractions, hence averages. A similar result was proved earlier for the impact factors
of a set of journals. Here we combine the two rank-order distributions, hereby eliminating the rank, yielding the functional
relation between the impact factor and the uncitedness factor. It is proved that the decreasing relation has an S-shape: first
convex, then concave and that the inflection point is in the point (μ′, μ) where μ is the average of the impact factors and
μ′ is the average of the uncitedness factors.
We present a mathematical derivation of the scale-dependence of the h-index. This formula can be used in two cases: one where the units are scale-dependent and one where the units are not scale-dependent. Examples are given.
If we have two information production processes with the same h-index, random removal of items causes one system to have a higher h-index than the other system while random removal of sources causes the opposite effect. In a Lotkaian framework we prove formulae for the h-index in case of random removal of items and in case of random removal of sources. In conclusion, we warn for the use of the h-index in case of incomplete data sets.
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.