# INTRODUCTION

 Published date 20 January 2005 Date 20 January 2005 DOI https://doi.org/10.1108/S1876-0562(2005)0000005002 Pages 1-6
INTRODUCTION
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
Zipf
s
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
direct).
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