Publication Date20 Jan 2005
The most facinating aspect of informetrics is the study of what we could call two-
dimensional informetrics. In this discipline one considers sources (e.g. journals,
authors, ...) and items (being produced by a source - e.g. articles) and their
interrelations. By this we mean the description of the link that exists between sources
and items. Without the description of this link we would have two times a one
dimensional informetrics study, one for the sources and one for the items. Essentially
in two-dimensional informetrics the link between sources and items is described by
two possible functions: a size-frequency function f and a rank-frequency function g.
Although one function can be derived from the other, they are different descriptions
of two-dimensionality. A size-frequency function f describes the number f(n) of
sources with n = 1, 2, 3, ... items while a rank-frequency function g describes the
number g(r) of items in the source on rank r = 1, 2, 3, ... (where the sources are ranked
in decreasing order of the number of items they contain (or produce)). So, in essence,
in f and g, the role of sources and items are interchanged. This is called duality, hence
f and g can be considered as dual functions.
Rank-frequency functions are well-known in the literature, especially in the
economics and linguistics literature, where one usually considers Pareto's law and
law, respectively, being power laws. Less encountered in the literature (except
in information sciences) is the size-frequency function. If studied, one supposes in
most cases also a power law for such a function, i.e. a function of the type
f(n)= C / na with a > 0. Such a function is then called the law of Lotka referring to its
introduction in the informetrics literature in 1926, see Lotka (1926). The law of Lotka
gives rise to a variety of derived results in informetrics, the description of them being
the subject of this book. That we choose a size-frequency function as the main study-
object is explained e.g. by its simplicity in formulation (in the discrete setting simpler
than a rank-frequency function since the latter uses ranks which have been derived
from the "sizes" n but also in the continuous setting, where sizes and ranks are taken
in an interval, the formulation of the size-frequency function is more appealing and
A size-frequency function also allows for a study of fractional quantities (see
Chapter VI), needed e.g. in the description of two-dimensional informetrics in which

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