authors produce half of the papers made by the total ofN authors. More generally: the topN(0<<1) authors produce a fraction (0<<1) of the papers made by the total ofN authors and the Price's law says that
. In this paper — using Lotka's law — we prove a mathematical relationship of in function of and the parameter (the mean number of papers per author) and investigate when
. More-over our reasoning uses the theory of the 80/20 rule as developed in: L. EGGHE, On the 80/20-rule,Scientometrics, 10 (1986) 55–68, thereby also showing the relation betwwen the 80/20-rules (being an arithmetical form of measuring elitarism) and Price's law (being a geometric form of measuring elitarism).
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.
The single publication H-index of Schubert is applied to the papers in the Hirsch-core of a researcher, journal or topic. Four practical examples are given and regularities are explained: the regression line of the single publication H-index of the ranked papers in the Hirsch-core is decreasing. We propose two measures of indirect citation impact: the average of the single publication H-indices of the papers in the Hirsch-core and the H-index of these single publication H-indices, defined as the indirect H-index. Formulae for these indirect citation impact measures are given in the Lotkaian context.
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.
I think that most of the problems mentioned in the GS paper are caused by natural evolutionary aspects of the discipline. It cannot be doubted that BIS is growing into a more and more professional research discipline. There are indeed problems of quality and of the fact that researchers have different origins. The first problem is evoluating in the right direction and the second one should be considered as an enrichment rather than as a negative fact. One must admit, nevertheless, that different subdisciplines will tend to live their own life, but that continuing contacts (such as joint conferences) remain important and are necessary for the further development of all these subdisciplines.
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.
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.
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 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.