Page 312 - Becoming Metric Wise

304 Becoming Metric-Wise

Consider a rank-frequency list or IPP subdivided into p groups, each
producing the same number of items. Then there exist numbers s 0 and
k . 1 such that the first group (containing the most productive sources)
consists of s 0 sources, the second group consists of s 0 k sources, the third
2
one of s 0 k sources and, generally, the ith group contains s 0 k i21 sources.
In the original formulation (Bradford, 1934) p 5 3. This is the smallest
possible number to observe a regularity. Indeed, the first group always
contains a certain number of sources and the second group contains
more, expressed by the number k . 1. The observation that the third
2
group contains precisely s 0 k sources points to a regularity. Table 9.1 illus-
trates this formalism. It shows 7 journals and the number of articles they
published on a given topic. Groups (shown in the right column) have 10
published items. The first group contains one journal (s 0 5 1); the second
group two, hence k 5 2. Now, this set of journals follows Bradford’s law
2
if the third group contains s 0 k 5 4 journals.
Later Leimkuhler (1967) showed that Bradford’s law could be refor-
mulated using the cumulative rank-frequency function R, known as
Leimkuhler’s function,
RðrÞ 5 a lnð1 1 brÞ (9.12)

where r denotes a rank and a and b are positive real numbers. Formula
(9.12) is the cumulative form of the rank-frequency function g.
The general (i.e., not only corresponding to α 5 2) cumulative rank
frequency form has no name, but was first formulated by Rousseau
(1988b), see also Egghe (2005). Egghe was the first to prove the mathe-
matical equivalence of all informetric laws (Egghe, 1985, 1990, 2005)
although partial proofs and a hypothesis about their equivalence can be

Table 9.1 An illustration of Bradford’s law
Ranked Number of published Number of journals in each
journals articles group
1 10 1
2 6 2
3 4
4 3 4
5 3
6 2
7 2